Oleg Vladimirovich Losev: Pioneer of Semiconductor Electronics (Celebrating One Hundred Years Since His Birth) M

Oleg Vladimirovich Losev: Pioneer of Semiconductor Electronics (Celebrating One Hundred Years since His Birth) M. A. Novikov

Losev was born in Tver into the family of a wagon works office worker, retired staff-captain of the Tzar army, and noble man. After he graduated from a Tver non-classical secondary school in 1920, he started to work at the Nizhni Novgorod Radio Laboratory (NNRL), where V.K. Lebedinskiœ became his supervi- sor of studies. After NNRL was closed in 1928, Losev, together with other leading collaborators, moved to Leningrad to work at the Central Radio Laboratory (CRL). From 1929 to 1933, at A.F. Ioffe’s invitation, Losev carried out investigations at the Ioffe Physicote- chnical Institute. From 1937 to 1942, Losev worked at the physics department of the Leningrad First Medical Institute. On January 22, 1942, Oleg Vladimirovich Losev died of starvation during the Leningrad blockade. The place of his burial is unknown. Up to the present time, only his works connected with the development of the crystadin were widely known in this country. Losev’s first work was devoted to the crystadin and was published in 1922. In that work, Losev showed that, when an additional dc voltage is applied to a crystal detector, it can operate as an amplifier or a generator of electromagnetic waves. In modern terms, this means that in this case a crystalline detector becomes a two-terminal device with a falling currentÐvoltage characteristic. It should be noted that a generating detector was first demonstrated in 1910 by the Englishman W.H. Eccles. On May 10, 2003, we celebrated the centenary of At that time, however, this interesting physical phe- the birth date of Oleg Vladimirovich Losev, an out- nomenon did not attract the attention of specialists in standing Russian scientist and inventor in the field of the radio field. Evidently, this is connected with the fact radio- and optoelectronics. that the author explained the mechanism of negative In his work at the Nizhni Novgorod Radio Labora- resistance on the basis of heat effects that occur at the tory and later in Leningrad at the Leningrad Central metalÐsemiconductor interface with allowance for the Radio Laboratory and in the physics department of the fact that the semiconductor resistance falls with First Medical Institute in the twenties and thirties of the increasing temperature. At that time, it was already last century, Losev made a number of important discov- known that this mechanism is the basis of the sounding eries and inventions that make him a pioneer in semi- arc, which is used to generate low-frequency radio conductor electronics. It should be noted, however, that waves in practical radio engineering. That was the rea- the importance of Losev’s outstanding scientific son why such devices were practically never used at achievements is underestimated both in this country and higher frequencies. abroad. In connection with the centenary of Losev’s Losev’s merit consists in that, using the example of birth, it is worth considering in detail and estimating his a zincite (ZnO) detector, by carrying out a series of very most outstanding scientific achievements from the mod- subtle experiments, he showed that in this case heat ern point of view in order to do this extraordinary scien- effects do not play any role and amplification is due to tist, who was ahead of his time, justice. electronic processes at the interface between a metallic

2 NOVIKOV tip and a semiconductor crystal. In particular, he dis- it was possible to create semiconductor devices that can covered that the zincite crystadin can generate and completely substitute for traditional radio lamps. It was amplify electromagnetic oscillations up to 10 MHz. At in the end of the 1920s that the idea of creating a solid- that time, this frequency range was not used even for state analog of a vacuum triode appeared. practical purposes. Losev’s merit consists in the fact As it has been learned recently that this idea was not that he applied this phenomenon in practice. He created foreign to Losev. In 1929Ð1931, while working on the a series of crystadin radio receivers which were used in experimental base of the Leningrad Physicotechnical a number of state radio stations. Crystadins were espe- Institute, he continued his studies (following the sug- cially popular with radio amateurs, who managed to gestion of A.F. Ioffe) of the new physical effects in establish even intercontinental radio contacts with the semiconductors that he discovered when working at help of simple crystal receivers and transmitters based NNRL. In particular, he investigated a semiconductor on a crystadin and energized from batteries with a volt- device identical to the structure of a point transistor. age of several volts. It was the simplicity and practical The operation of this device is known to be based on the value of the crystadin that caused a wide wave of inter- control of current flowing between two electrodes with est in it in the world. Newspapers and respectable sci- the help of an auxiliary electrode. Losev actually entific journals in Europe and America wrote about it as observed this effect, but, unfortunately, the total gain fac- of a sensational invention in the mid 1920s. Many sci- tor was insufficient to amplify a signal. However, for this entists foresaw that the coming revolution in radios purpose, he used only a silicized carbon crystal (SiC) and would be connected with Losev’s crystadin. did not use a zincite crystal (ZnO), which has signifi- Unfortunately, at that time, Losev’s discovery was cantly better characteristics in a crystadin amplifier. not properly developed. Notwithstanding his heroic Until recently, it was considered that, after being efforts, Losev failed to eliminate the main practical forced to resign from the Physicotechnical Institute, drawback of the crystadin, namely, its unstable opera- Losev did not return to the idea of semiconductor tion due to mechanical contact of a metal tip with a crys- amplifiers. However, the existence of a very interesting tal. Furthermore, in the mid 1920s, the crystadin could document, written by Losev himself, has recently not compete with vacuum radio lamps, because that was become known. This document is dated July 12, 1939, the period of their most intensive improvement and all and is currently stored at the Polytechnic Museum. The the practical problems regarding their usage in radio document, titled Oleg Vladimirovich Losev’s Biogra- engineering at that time were solved. These advances, in phy, contains interesting facts from his life and a list of fact, were due, to a significant degree, to the studies per- his scientific achievements. The following lines are of formed at NNRL, where Losev worked. special interest: “It has been established that a three- Despite the efforts of well-known physicists, includ- electrode system analogous to a triode and showing ing Nobel Prize laureate R.A. Millikan, as well as the negative resistance, like a triode, can be built on the investigations of Losev himself, the mechanism of the basis of semiconductors. At the present time, I am pre- falling currentÐvoltage curve of the crystadin was not paring these findings for publication.” puzzled out at that time. Now, it became clear that an Unfortunately, the fate of these findings has not been understanding of this mechanism could not be gained established so far; they could have completely changed without quantum mechanics. However, in the mid the notion of transistor invention history, one of the 1920s, its physical basis had not yet been created and most revolutionary inventions of the twentieth century the band theory of semiconductors was developed only Other important scientific merits of Losev are con- in the early 1930s. nected with his investigations in the field of electrolu- Unfortunately, the mechanism of Losev’s zincite minescence and light-emitting diodes (LEDs). Losev’s crystadin has not been explained so far. The point is investigations in the field of electroluminescence have that, at the present time, about a dozen physical pro- been well known since the 1920s, and those studies are cesses are known that lead to the phenomenon of nega- referred even now. In the 1920s, the phenomenon of tive resistance. Many specialists link Losev’s crystadin electroluminescence was even called Losev light effect with Esaki junction, but so far no experiments (Lossew Licht) in the West for some time. For this rea- confirming this hypothesis have been performed. It son, Losev is justly considered abroad to be a pioneer would be interesting to repeat Losev’s experiments in the field of electroluminescence. However, it is not with zincite now using modern methods of investiga- known whether Losev was the inventor of LED. He was tion. This would be especially interesting now as great the first to see huge perspectives in such light sources interest is being shown in this crystal by optoelectron- and point out their high brightness and high response ics engineers. speed. He is also the owner of the first patent for the We should reject the opinion of science historians invention of a device with an electroluminescent light that the interest in Losev’s crystadin had completely source (light relay). disappeared by the end of the 1920s. Attempts to use At the end of the 1970s, when electroluminescent the crystadin were made later as well, but the main light sources began to be widely used in the West, point is that Losev’s crystadin phenomenon proved that H.F. Ives came across a small article by H.J. Round

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OLEG VLADIMIROVICH LOSEV: PIONEER OF SEMICONDUCTOR ELECTRONICS 3

“A Note on Carborundum” in Electrical World, 49, 308 ent, because quantum solid-state theory had not been (1907), in which the author (research worker at the created yet (it appeared only ten years later). Now it is Marconi laboratory) reported that he had observed clear that progress in semiconductor electronics is luminescence from a silicized carbon (SiC) detector impossible without quantum theory of the semiconduc- contact under the influence of an external electric field. tor structure. Furthermore, at that time, there was prac- There was no other information about the luminescence tically no technical basis for experimental investiga- and about the physics of this phenomenon in the article. tions in the field of the physics of semiconductors. Even At that time, nobody paid any attention to it, and this greater amazement comes from Losev’s intuition, his article did not influence subsequent investigations in art and experimental talent, which allowed him to the field of electroluminescence. However, some spe- achieve remarkable results. cialists, including Russian ones, consider this author to In particular, from the very beginning, he saw the be the discoverer of the electroluminescence phenome- common physical nature of the crystadin and injection non. As for Losev, he not only discovered this phenom- luminescence, thereby being far ahead of his time. The enon independently, but also carried out a detailed point is that, after Losev, investigations of semiconduc- investigation of it on the example of a silicized carbon tor detectors of electroluminescence were conducted (SiC) crystal. For example, he discovered that in this separately and independently by different groups of sci- case there are two different physical phenomena entists. Some of them studied only the phenomena con- observed at different contact voltage polarities. Losev nected with rectification in semiconductor structures, discovered not only injection electroluminescence which led to the invention of transistors in 1947 and (luminescence II in his terms), which at present time tunnel diodes. forms the basis of light-emitting diodes and semiconductor lasers, but also the electroluminescence that is Independently, investigations of electroluminescent emitted before the onset of breakdown (luminescence I), light sources were performed. An analysis of their which is also widely used in creating new electrolumi- results shows that, for over twenty years after Losev’s nescent displays. Later on, luminescence I was also dis- studies, no progress was achieved toward an under- covered by French scientist G. Destriau, and now it is standing of the physics of this phenomenon. The major- called the Destriau effect, though Destriau himself ity of the studies carried out over this period were attributed the discovery to Losev. Furthermore, Losev devoted to devices based on pre-breakdown electrolu- managed to advance very far in understanding the phys- minescence with the aim of creating different kinds of ics of these phenomena even when the band theory of optic displays. Only in 1951 (almost thirty years after semiconductors had not been discovered yet. Thus, Losev) did K. Lehovec with collaborators show that modern supporters of attributing the discovery to rectification and electroluminescence have a common Round hardly have the right to dispute the outstanding nature linked with the behavior of charge carriers in pÐ contribution of our fellow countryman to this field of n junctions and that electroluminescence is connected physics and especially to the invention of LED. For with the recombination of electrons and holes in these example, Popov and Marconi are justly considered to junctions. It should be noted that, in his work, Lehovec be the inventors of the radio, though it is well known refers first of all to all Losev’s works devoted to elec- that Hertz was the first to observe radio waves. There troluminescence. are many analogous examples in the history of science. It was this point of view that allowed Losev to sig- In evaluating Losev’s research activities, it should nificantly advance the understanding of the physics of be noted that, above all, he was an outstanding physicist semiconductor contacts. By combining the optical and and experimentalist. Although he worked under excep- electrophysical methods of investigation of these con- tionally difficult conditions in the early 1920s, he tacts and using a silicized carbon contact as an exam- achieved remarkable scientific results. E.E. Loebner, a ple, he was able to develop a layered model of its struc- well-known American scientist in the field of electrolu- ture with a detailed description of each layer at the end minescence, wrote the following about Losev in his arti- of the 1920s. It is surprising that this model differs only cle “Subhistory of the Light-Emitting Diode,” the most insignificantly from the modern model. part of which was devoted to an analysis of Losev’s con- Highly valuing Losev’s achievements, we should tribution to the study of electroluminescence and LEDs: note the following fact. Losev stood at the beginning of “By his pioneering investigations in the field of Light- the probe microscopy of semiconductor structures, Emitting Diodes and photodetectors, he contributed to which has recently drastically changed both research the future progress of light communication. His investi- methods and the technology of semiconductor struc- gations are so accurate and his publications are so clear tures. In 1930Ð1931, Losev carried out, at a very high that it is easy to imagine now what was happening in his experimental level, a series of experiments with angle laboratory at that time. His intuitive choice and the art of laps, which expand the zone under investigation, and experiment are astonishing” (see list of publications ded- with a system of electrodes, which were included into a icated to Losev). compensation-measuring circuit in order to measure It should be added that Losev worked at a time when the potentials at different points of a cross section of the the physics of semiconductors was basically nonexist- layered structure. By moving a thin metal tip across a

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

4 NOVIKOV lap, he showed, to an accuracy of 1 µm, that the surface usual, his intuition did not fail him this time. Losev felt layer of a crystal has a complex structure. He revealed that the silicon crystal had considerable promise. that there is a 10-µm-thick active layer in which injec- The attack of Nazi Germany put scientific investigation electroluminescence occurs. Based on his investi- tion into the background, but Losev wanted to finish the gations, Losev assumed that the reason for unipolar work he had begun and he refused to leave the city. conductivity is the difference between the conditions Apparently, he managed to finish the work and send it under which electrons move on either side of the active to the Journal of Technical Physics in Leningrad. By layer (in modern terms, different types of conductivity). that time, however, the editorial office had already been By experimenting with three or more probe electrodes evacuated. Unfortunately, after the war ended, no traces located in these regions, he confirmed this assumption. of the article were found, and now we can only specu- From the modern point of view, these investigations late about its contents. are undoubtedly Losev’s greatest achievement as a Among other discoveries, which were also not appre- physicist. His invention of LEDs (according to Losev’s ciated by Losev’s contemporaries, we should note the terminology, electronic generators of light) is difficult effect of transgeneration observed by him in multiloop to overestimate. LEDs are the undoubted basis of mod- radio circuits with nonlinear elements. These discoveries ern optoelectronics. Undoubtedly, the significance of were a significant contribution to the development of the discovery of LEDs can be compared to that of the nonlinear radio engineering, but, unfortunately, they transistor or laser in its influence on scientific and tech- have not yet been properly evaluated and developed. nical progress. The above analysis of the scientific achievements It should also be noted that Losev made other impor- and discoveries of Losev shows that he was an tant discoveries less known even to specialists. He extremely talented scientist in the field of semiconduc- made a considerable contribution to semiconductor tor science and engineering. We can definitely say that materials technology as well. Losev discovered and each scientific and technical undertaking in the field of experimentally realized the method of arc remelting of physics of semiconductors made by Losev in the 1920s semiconductor materials on the example of zincite, and 1930s was developed later on into an independent which made it possible to considerably improve the perspective branch. This is the reason why Losev is con- characteristics of the zincite crystadin. In the 1930s, sidered a pioneer in modern radio and optoelectronics. Losev carried out a series of studies on the photoeffect Unfortunately, after the war, the investigations in semiconductor structures. In these pioneering stud- started by Losev were not continued and were gradu- ies, it was shown that it is possible to obtain maximally ally forgotten. This was connected with the fact that high quantum efficiency in such photodetectors. It was Losev had no pupils who could carry on his investiga- these findings that determined modern progress in tions. Another reason was the difficult post-war situa- developing semiconductor photodetectors. Losev con- tion. Apparently, due to Losev’s studies, this country tinued to conduct these investigations during the Lenin- had a real chance to become the leader in the field of grad blockade until his death. semiconductor electronics in pre-war years. The fact He discovered the photoeffect in an illuminated sili- that Losev’s investigations were not developed further cized carbon detector in 1924 while working at NNRL. in their time accounts for our lagging behind in the field Using his method of laps and probe microscopy, he of radios and optoelectronics. convincingly proved that the effect observed in sili- In connection with the scientist’s centenary, the staff cized carbon is indeed due to a photovoltage and the of the NNRL museum is preparing a collection of arti- photovoltage appears in a 1- to 3-µm-thick part of the cles devoted to O.V. Losev’s life and scientific activity active layer. By investigating powder samples, he dis- for publication. In particular, this collection will con- covered a very interesting photo-dielectric effect contain the article by B.A. Ostroumov “O.V. Losev as the sisting in the fact that when the SiC contact is illumi- inventor of crystadin,” which was written in the begin- nated its capacity also changes. Already in the 1930s, ning of the 1950s but was never published. I.V. Kurchatov pointed out the value of this series of Losev’s studies. PUBLICATIONS DEDICATED TO LOSEV Another of Losev’s merits is his pioneering investigations of the photoelectric properties of silicon. In 1. O. V. Losev, At the Origin of Semiconductor Engineer- order to choose a material for the production of photo- ing, Ed. by G. A. Ostroumov (Nauka, Leningrad, 1972). cells and photoresistors, Losev examined more than 2. A. G. Ostroumov and A. A. Rogachev, in Physics: Prob- 90 substances. In particular, the photosensitivity of sil- lems, History, People, Ed. by V. M. Tuchkevich (Nauka, icon was found to be significant. At the end of the Leningrad, 1986). 1930s, he intuited that this material is very perspective. 3. E. E. Loebner, IEEE Trans. Electron Devices 23 (7), 675 (1976). In the beginning of 1941, Losev started to work on a new theme, “The method of electrolytic photoresistors: Photosensitivity of certain silicon alloys.” As Translated by A. Titov

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Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 10Ð12. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 15Ð17. Original Russian Text Copyright © 2004 by Svetlov, Chalkov, Shengurov, Drozdov, Krasil’nik, Krasil’nikova, Stepikhova, Pavlov, Pavlova, Shilyaev, Khokhlov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Structural and Photoluminescence Properties of Heteroepitaxial Silicon-on-Sapphire Layers S. P. Svetlov*, V. Yu. Chalkov*, V. G. Shengurov*, Yu. N. Drozdov**, Z. F. Krasil’nik**, L. V. Krasil’nikova**, M. V. Stepikhova**, D. A. Pavlov***, T. V. Pavlova***, P. A. Shilyaev***, and A. F. Khokhlov***† *Physicotechnical Research Institute, Nizhni Novgorod State University, Nizhni Novgorod, 603950 Russia e-mail: [email protected] **Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia ***Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950 Russia

Abstract—The growth of erbium-doped silicon layers on sapphire substrates through sublimation molecular- beam epitaxy is studied for the ﬁrst time. Structural analysis data are given, and the luminescence properties of ° layers are discussed. Heteroepitaxial silicon-on-sapphire layers grown at a temperature Ts = 600Ð700 C are found to be fairly perfect in structure. Photoluminescence spectra show a peak at a wavelength of 1.54 µm associated with intracenter transitions in the rare earth Er3+ ion. © 2004 MAIK “Nauka/Interperiodica”.

† 1. INTRODUCTION 2. EXPERIMENTAL

One of the promising fields in modern micro- and Sapphire plates with the (1102 ) orientation were nanoelectronics is the fabrication of devices and “sili- used as substrates. Prior to the deposition of Si layers, con-on-insulator” structures including heteroepitaxial the plates were annealed at temperatures of 1200Ð silicon-on-sapphire (SOS) films. One of the advantages 1400°C for 30Ð90 min directly inside the growth cham- of such structures is their high resistance to radiation ber. To form Si and Er atomic beams, a sublimation and thermal damage and the low power consumption of source (cut from an Er-doped silicon ingot) was heated integral microcircuits based on them [1]. The realiza- to a temperature of ~1330°C by passing an electric cur- tion of multifunctional microprocessor circuits on sap- rent through it [5]. In a number of experiments, phire substrates and the improvement of their integra- undoped Si layers were grown on sapphire using KDB- tion level require further development of optoelectronic 15-grade silicon heated to ~1380°C. The deposition circuits. In this connection, Si-based structures with rate was 0.08Ð0.1 nm/s. The substrate temperature was various rare earth dopants are of particular interest [2]. varied from 500 to 800°C. The residual pressure during The basic technique of preparing SOS structures is the growth of the layers did not exceed 1 × 10Ð7 Torr. crystallization from the vapor phase with the involve- The thicknesses of the grown Si layers were 0.25 to ment of chemical reactions [3]. However, the high dep- 0.75 µm. osition temperature (~1000°C) results in the formation The structure of the deposited layers was analyzed of compressive stresses in Si layers because of fairly using electron and x-ray diffraction. An ÉMR-102 elec- large differences in the values of the coefficients of lin- tron diffractometer was used in the reflection mode at a ear thermal expansion of silicon and sapphire. In order glancing incident angle and an acceleration voltage of to increase the crystal perfection, the SOS structures 100 kV. X-ray diffraction spectra were recorded with are grown by using molecular-beam epitaxy (MBE) [4]. the aid of a DRON-4 diffracrometer using a Ge(400) At low growth temperatures, the effect of a difference monochromator and CuKα radiation. The morphology in the thermal expansion coefficients between these 1 materials becomes minimal and the density of defects of the layer surface was analyzed using an Accurex TMX-2100 atomic-force microscope. Photolumines- in epitaxial layers decreases. cence was measured using a modernized KSVU-23 Our aim was to study the possible growth of Er- device with an MDR-23 base monochromator. Photolu- doped Si epitaxial layers on sapphire by using the sub- minescence (PL) was excited by an argon laser limation MBE method. Luminescence of these layers (514.5-nm line) with a pumping power of ~100 mW. A occurs at a wavelength of 1.54 µm. cooled, highly sensitive EO-817A Ge detector and a standard “lock-in” detection technique were used to † Deceased. record photoluminescence spectra. The spectra were

STRUCTURAL AND PHOTOLUMINESCENCE PROPERTIES 11

11.19 nm

0 nm

Fig. 1. Electron reﬂection diffraction pattern of a Si-on-sapphire structure. (a) 1 µm measured at temperatures of 77 and 300 K with a reso- 77.72 nm lution of ~6 nm.

3. RESULTS AND DISCUSSION 3.1. Structure of the Grown Layers We studied the inﬂuence of the predepositional 0 nm annealing temperature of a substrate and the growth temperature on the structure of the grown Si layers. Sil- icon was evaporated from an undoped source. After annealing of a substrate at a high temperature (~1400°C) for 30 min, Kikuchi lines and stripes were observed in the electron diffraction patterns (Fig. 1), which is indicative of high structural perfection of the 1 µm surface region of the Si layer. As the growth tempera- (b) ture was increased, the contrast of Kikuchi patterns became higher; i.e., the structure of an epitaxial layer was improved. At the same time, Kikuchi patterns were Fig. 2. Atomic-force images of the silicon layer surfaces barely visible in the initial sapphire substrate. This was grown on sapphire substrates preannealed at (a) 1400 and (b) 1200°C. probably due to the sapphire substrate surface layer being damaged by mechanical polishing. Silicon layers grown on substrates annealed at 1400°C have a rather smooth surface (Fig. 2a), while the surface of epitaxial layers deposited on substrates 350 annealed at 1200°C looks more rough (Fig. 2b). It seems likely that in the latter case the temperature did not prove high enough to remove carbon and oxygen contaminations from the sapphire surface. 250 ° On the substrates annealed at 1400 C, silicon was FWHM = 0.24° deposited in layers. X-ray diffraction patterns show that at low growth temperatures (500Ð550°C) Si layers are 150 , arb. units preferably oriented along the (110) plane, while at I growth temperatures above 600°C, along the (100) plane. The most intense x-ray diffraction peak for such 50 ° orientation was observed in the layers grown at 700 C. 0 A typical rocking curve obtained for a Si(100) layer is shown in Fig. 3. 33.5 34.0 34.5 35.0 After studying the epitaxy of undoped Si layers on ω, deg sapphire, we grew Er-doped layers. The growth temperature of these layers was 600°C. This temperature was specially chosen somewhat lower than the optimal Fig. 3. X-ray diffraction rocking curve [Si(400) reﬂection] ° temperature for obtaining structurally perfect layers of a Si epitaxial layer grown at Ts = 700 C.

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12 SVETLOV et al.

2400 1.59 µm layers grown on sapphire substrates preliminary T = 77 K 1.54 µm annealed at 1200 and 1400°C. The x-ray diffraction λ 0 = 514.5 nm data for these samples give rocking-curve half-widths L0 = 100 mW equal to 0.4° and 0.36° and relative Si(400) reﬂection peak intensities equal to 400 and 3400, respectively. It 1600 1 can be seen that the parameters of the PL line at 1.59 µm correlate closely with the defect structure 1.07 µm parameters of the layers. The photoluminescence of the sapphire substrate in SOS structures reveals itself only 800 2 as a weak signal in the range 0.9Ð1.2 µm (curve 4 in Fig. 4), which is also present in the spectra of epitaxial 3 PL intensity, arb. units layers. It should be noted that, for the structures stud- 4 ied, the PL spectra virtually do not contain the characteristic dislocation-induced (D1ÐD4 [7]) lines 0 observed, as a rule, in silicon with a high density of dis- 0.8 1.2 1.6 2.0 locations and structural defects. The PL of SOS struc- λ, µm tures in the range 1.5Ð1.7 µm considerably decreases in intensity with increasing temperature and becomes vir- Fig. 4. Photoluminescence spectra of SOS structures. tually unobservable at 300 K. (1) Er-doped Si layer; (2, 3) undoped Si layers of various defect structure grown on substrates after prior annealing at 1200 and 1400°C respectively; and (4) sapphire substrate. 4. CONCLUSIONS Thus, we have shown that sublimation MBE pro- µ (700°C) in order to avoid the formation of silicide com- vides a means of growing perfect thin (~0.5- m-thick) Si layers on sapphire, including Er-doped layers lumi- pounds in Si layers. The Er concentration in the layers µ was about 5 × 1018 cmÐ3. nescent at a wavelength of 1.54 m.

3.2. Photoluminescence Features of SOS Structures ACKNOWLEDGMENTS This study was supported in part by the Russian The results of photoluminescence studies of Foundation for Basic Research (project nos. 01-02- undoped and Er-doped SOS structures are shown in 16439, 02-02-16773) and the Analytical Coordination Fig. 4. At a temperature of 77 K, the PL spectrum of an Center of Innovation, Science, and Engineering Pro- Er-doped SOS structure in the wavelength range 1.5Ð µ grams (“Fundamental Spectroscopy,” project 1.7 m contains a fairly intense signal with two peaks, no. 08.02.043). at 1.54 and 1.59 µm (Fig. 4). The PL peak at 1.54 µm, considering its position and narrowness, can be assigned to the transition from an excited to the ground REFERENCES 3+ state in the rare earth Er ion 4f shell (transition 1. D. Mead and J. Hine, Rep. Prog. Phys. 8 (3), 327 (1987). 4 4 I13/2 I15/2). The other, more intense, line at 2. N. A. Sobolev, Fiz. Tekh. Poluprovodn. (St. Petersburg) 1.59 µm is considerably broadened and, judging by its 29, 1153 (1995) [Semiconductors 29, 595 (1995)]. position and relative intensity with respect to the ﬁrst 3. V. S. Pankov and M. B. Tsybul’nikov, Epitaxial Silicon line, is obviously not related to transitions in the rare Layers on Dielectric Substrates and Devices on Their earth impurity center. Its shape and width suggest that Basis (Énergiya, Moscow, 1979). this PL line comes most probably from defect com- 4. E. D. Richmond, J. G. Pelligrino, M. E. Twigg, et al., plexes in the stressed silicon layer or from impurity- Thin Solid Films 192, 287 (1990). center complexes, such as the known defect complexes 5. S. P. Svetlov, V. Yu. Chalkov, and V. G. Shengurov, Prib. consisting of carbon and oxygen atoms (C and P lumi- Tekh. Éksp., No. 4, 141 (2000). nescence lines [6]), whose content can be large in epi- µ 6. W. Kuerner, R. Sauer, A. Doerner, and K. Thonke, Phys. taxial silicon layers. Indeed, the peak at 1.59 m was Rev. B 39 (18), 13327 (1989). also observed in PL spectra of the SOS structures not 7. R. Sauer, J. Weber, and J. Stolz, Appl. Phys. A 36, 1 doped with the rare earth impurity (not containing the (1985). line at 1.54 µm) and the intensity of this peak increased with degradation of the crystalline layer structure. For comparison, Fig. 4 shows the PL spectra of Si epitaxial Translated by A. Zalesskiœ

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 101Ð103. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 102Ð104. Original Russian Text Copyright © 2004 by Shengurov, Svetlov, Chalkov, Andreev, Krasil’nik, Kryzhkov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Effect of Growth Conditions on Photoluminescence of Erbium-Doped Silicon Layers Grown Using Sublimation Molecular-Beam Epitaxy V. G. Shengurov*, S. P. Svetlov*, V. Yu. Chalkov*, B. A. Andreev**, Z. F. Krasil’nik**, and D. I. Kryzhkov** * Physicotechnical Research Institute, Nizhni Novgorod State University, Nizhni Novgorod, 603950 Russia e-mail: [email protected] ** Institute of the Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia

Abstract—Erbium-doped epitaxial silicon layers were grown using two different growth techniques, namely, commonly used molecular-beam epitaxy (MBE) and solid-phase epitaxy (SPE). It is shown that an erbium- doped silicon epitaxial layer deposited through SPE on a cold substrate and subsequently annealed displays a more intense photoluminescence at a wavelength of 1.54 µm than do MBE-grown layers. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION Our aim was to obtain SPE-grown heavily Er-doped Si layers exhibiting photoluminescence at a wavelength There has been an increasing number of publica- of 1.54 µm. tions devoted to the study of Er-doped silicon because of the application potential of this material in Si-based optoelectronic devices working at a wavelength of 2. EXPERIMENTAL 1.54 µm [1]. One of the features required of this material intended for use in such silicon-based devices is a Er-doped epitaxial layers were grown in an ultrahigh content of optically active erbium centers. For Er high-vacuum MBE chamber with the aid of the device doping of Si through ion implantation, high-energy shown in Fig. 1 [7]. Si was evaporated from a sublima- ions (0.5Ð5 MeV) are used. In this case, defects are tion source in the form of a rectangular bar heated by formed that survive in part even after a long-term passing an electric current, and Er was also evaporated annealing and cause the rare-earth impurity to precipitate [2]. In the course of ion implantation, as well as in other doping techniques, the interaction of Er and Si 7 5 6 1 atoms results in the formation of optically inactive silicide compounds. It has been established that, in order 10 to suppress the formation of such Er and erbium silicide 2 precipitates, Er doping should be performed at low temperatures and be accompanied by co-doping with oxygen to form optically active Er3+-containing centers [3]. 2 Molecular-beam epitaxy (MBE) with co-evaporation of Si and Er makes it possible to grow layers with a total Er concentration up to 1022 cmÐ3 [4]. However, the photoluminescence (PL) intensity in layers with an 2 Er concentration above 1018 cmÐ3 decreases, probably 9 due to the formation of structural defects [4, 5]. 3 Another method allowing one to grow heavily 4 8 doped Si layers is solid-phase epitaxy (SPE), which consists of two stages, namely, precipitation of a layer Fig. 1. Device for Si : Er layer growth (schematic). (1) Erbium plate, (2) current carriers, (3) molybdenum at low temperatures (where the impurity segregation is springs, (4) molybdenum fasteners, (5) silicon bar, (6) sili- kinetically suppressed) and subsequent annealing of con spacer, (7) stationary screen, (8) substrate, (9) molybde- the amorphous Si ﬁlm [6] num clamps, and (10) movable screen.

102 SHENGUROV et al. ing an electric current. After annealing of a substrate at 0.36 T = 1250°C for 10 min, Si layers were grown through 0.32 6500 MBE at 500°C or through SPE on a heated substrate 0.28 with a subsequent in situ annealing. 0.24 PL spectra were measured at 77 K with the aid of a Fourier BOMEM DA3 spectrometer with a resolution 0.20 of 1 cmÐ1 under pumping Ar+ laser radiation (wave- 0.16 length λ = 514.5 nm, power 80 mW), illuminating the 0.12 epitaxial-layer surface. The layer structure was examined using electron diffraction. 0.08 0.04 3. RESULTS AND DISCUSSION 0 Photoluminescence intensity, arb. units 3.1. Molecular-Beam Epitaxy 6000 6200 6400 6600 Wave number, cm–1 After annealing of a substrate, a buffer undoped Si layer ~0.1 µm thick was grown at 1050°C. Then, the ° Fig. 2. PL spectrum of an MBE-grown structure recorded at temperature was reduced to Ts = 550 C, the chamber T = 77 K for pumping Ar laser power P = 80 mW. was ﬁlled with oxygen to a pressure of 9.5 × 10Ð8 Torr, and an Er-doped layer ~0.5 µm thick was grown. The electron concentration in the layer was measured with a CÐV proﬁlometer to be about 1017 cmÐ1. Figure 2 shows the PL spectrum for this structure measured at liquid-nitrogen temperature. A broad band with a peak at 6500 cmÐ1 is typical of Er3+-ion PL spectra of Si : Er/Si structures grown through sublimation MBE with a metallic Er source and having a higher concentration of oxygen and carbon in comparison to that of Er.

3.2. Solid-Phase Epitaxy ≈ An amorphous Er-doped Si layer was grown at Ts 150°C. The layer growth was periodically interrupted (‡) to ﬁll the chamber with oxygen to a pressure of 5 × 10−5 Torr. After the layer thickness reached ~50 nm, the substrate temperature was increased up to 800°C and the system was annealed for 30 min. Figure 3 shows electron diffraction patterns of the layer surfaces grown on (111)- and (100)-oriented substrates. It can be seen that the layers formed on a (100) substrate have more perfect structure. The erbium PL spectrum for an SPE-grown Si epitaxial layer is shown in Fig. 4. This PL spectrum contains a series of strong narrow lines associated with the 4 4 3+ I13/2 I15/2 transition in the 4f shell of the Er ion (b) forming a known single radiative cubic center [8]. Such a spectrum is usually characteristic of Er in a silicon single crystal with a low oxygen concentration in com- Fig. 3. Electron diffraction patterns taken from the layer parison with that of Er. However, the integrated Er3+- surfaces grown on (a) (111)- and (b) (100)-oriented sub- ion PL intensity in the SPE-grown structure is twice strates. that in the MBE-grown structure. According to the existing models of the growth of an amorphous silicon layer through SPE on a single-crys- from a sublimation source cut from a metal foil. A rect- tal substrate in vacuum, the epitaxial-crystallization angular Si plate cut along the (100) or (111) plane from front moves from the interface between the single crys- a Si KDB-12-grade Si single crystal served as a sub- tal and the amorphous layer towards the layer surface strate. A substrate and the sources were heated by pass- during annealing [9]. At an annealing temperature of

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EFFECT OF GROWTH CONDITIONS ON PHOTOLUMINESCENCE 103

4. CONCLUSIONS 1.2

6504 Thus, the solid-phase epitaxy method can be used to form a heavily Er-doped layer in an Si ﬁlm deposited in ultrahigh vacuum. The photoluminescence observed 0.8 from such a layer is more intense than that from an MBE-grown layer.

0.4 ACKNOWLEDGMENTS This study was supported in part by the Russian Foundation for Basic Research (project nos. 01-02- 16439, 02-02-16773) and the Ministry of Industry, Sci- 0 Er-cubic ence, and Technology of the Russian Federation (State Photoluminescence intensity, arb. units 6000 6200 6400 6600 Contract nos. 40.020.1.1.1161, 40.020.1.1.1159). Wave number, cm–1 REFERENCES Fig. 4. PL spectrum of an SPE-grown structure. The spectrum was taken under the same conditions as for the spec- 1. N. A. Sobolev, Fiz. Tekh. Poluprovodn. (St. Petersburg) trum shown in Fig. 2. 29, 1153 (1995) [Semiconductors 29, 595 (1995)]. 2. A. Polman, J. Appl. Phys. 82, 1 (1997). 600°C, the amorphous Si crystallizes on the single- 3. Y. Ho Xie, E. A. Fitzgerald, and Y. J. Mii, J. Appl. Phys. crystal substrate due to epitaxial ordering of atoms of 70, 3223 (1991). amorphous silicon near the interface, whereas at a tem- 4. H. Efeoglu, J. H. Evans, T. E. Jackmann, et al., Semi- perature of 800°C additional nucleation and growth of cond. Sci. Technol. 8, 236 (1993). randomly oriented crystallites occurs in the bulk of the 5. R. Serna, M. Lohmeier, P. M. Zagwijn, et al., Appl. Phys. amorphous Si. The epitaxial crystallization rate at Lett. 66, 1385 (1995). 800°C is 2.2Ð10 nm/min. Due to such a high crystalli- 6. V. G. Zavodiskii and A. V. Zotov, Phys. Status Solidi A zation rate, part of the layer surface becomes occupied 72, 391 (1982). by the single-crystal phase and the remainder by the 7. S. P. Svetlov, V. Yu. Chalkov, and V. G. Shengurov, Prib. polycrystalline phase upon completion of the anneal- Tekh. Éksp., No. 4, 141 (2000). ing. The effect of oxygen on the reduction of crystalli- 8. H. Przybylinska, W. Jantsch, Yu. Stepikhova, et al., Phys. zation rate was reported in [10]. However, in our exper- Rev. B 54, 2532 (1996). iments, when crystallization was interrupted and oxy- 9. I. G. Kaverina, V. V. Korobtsov, and V. G. Lifshits, Thin gen was let in, it is likely that a thin layer of adsorbed Solid Films 177, 101 (1984). gas was formed and captured by the growing layer only 10. C. W. Nogee, J. C. Bean, C. Foti, and J. M. Poate, Thin partly. As a result, the total amount of oxygen intro- Solid Films 81, 1 (1981). duced into the layer was very small. This may be the cause of the changes in the Er3+-ion PL spectra observed in SPE-grown Si layers. Translated by A. Zalesskiœ

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 104Ð108. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 105Ð109. Original Russian Text Copyright © 2004 by Kashkarov, Kamenev, Lisachenko, Shalygina, Timoshenko, Schmidt, Heitmann, Zacharias.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

High-Efficiency Erbium Ion Luminescence in Silicon Nanocrystal Systems P. K. Kashkarov*, B. V. Kamenev*, M. G. Lisachenko*, O. A. Shalygina*, V. Yu. Timoshenko*, M. Schmidt**, J. Heitmann**, and M. Zacharias** *Faculty of Physics, Moscow State University, Vorob’evy gory, Moscow, 119992 Russia **Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, Halle, 06120 Germany

Abstract—The photoluminescence spectra and kinetics of both erbium-doped and undoped multilayer structures of quasi-ordered silicon nanocrystals in a silicon dioxide matrix were studied. It was shown that the optical excitation energy of silicon nanocrystals 2Ð3 nm in size can be practically completely transferred to Er3+ ions in the oxide surrounding the nanocrystals, with its subsequent radiation at 1.5 µm. Possible reasons for the high excitation efﬁciency of the Er3+ ions are discussed, and the conclusion is drawn that the Förster mechanism is dominant in the energy transfer processes occurring in these structures. © 2004 MAIK “Nauka/Inter- periodica”.

1. INTRODUCTION the erbium luminescence is practically independent of the nature of the matrix because of the “operating” Er3+ Considerable attention has been focused in recent 3+ 4f shell being screened by the outer electronic shells, years on Er ion luminescence in crystalline and amor- the ion excitation efficiency can be controlled by prop- phous silicon (see, e.g., [1, 2]). This interest stems from erly varying the properties of the matrix, for instance, the need to develop silicon devices capable of emitting µ 4 the width of its band gap, and/or the density of elec- efficiently at a wavelength of 1.54 m (the I13/2 tronic states of the defects and impurities contained in 4 3+ I15/2 transitions in the inner 4f shell of the Er ion), the matrix [1, 3]. This can be readily reached in nc-Si which corresponds to the maximum transparency of structures, because the band gap of nanocrystals can be fiber communication lines. The development of such varied within broad limits by properly varying their optoelectronics devices is hindered, however, by a dimensions [12, 13]. Furthermore, in Si nanocrystals number of still unsolved problems. For instance, if 3+ one can simultaneously attain both a good carrier local- crystalline silicon (c-Si) is used as a matrix for Er , ization in small space regions near the Er atoms and strong thermal quenching of the erbium luminescence 3+ fairly long (hundreds of microseconds) lifetimes of the is observed, which is caused by the nonradiative Er electronic excitation [12, 13]. In this case, the energy ion deexcitation originating from the energy transfer released in recombination of a photoexcited electronÐ back to the matrix [3]. As a result, the room-tempera- 3+ ture luminescence quantum efficiency of c-Si : Er sam- hole pair can be efficiently transferred to the Er ion. ples turns out to be very low. The 1.5-µm photolumi- Indeed, samples of erbium-doped nc-Si in a SiO2 nescence (PL) and electroluminescence of erbium- matrix exhibit an intense and stable Er3+ ion PL even at doped amorphous hydrogenated silicon (a-Si : H : Er) room temperature [9, 10]. Note that the efficiency of the features a fairly weak temperature dependence [4]. Fur- PL and its lifetime depend strongly on the technique by thermore, analysis of the PL kinetics in a-Si : H : Er which the nc-Si/SiO2 structures were prepared, as well suggests that the energy of the electronÐhole pairs is as on the size of the Si nanocrystals [9]. This suggests transferred to Er3+ ions in fairly short (submicrosecond- that layers of quasi-ordered silicon nanocrystals in nc- scale) times, which accounts for the high efficiency of Si/SiO2 superlattices, which permit easy tailoring of the their excitation [5Ð7]. Because, however, of the exist- nanocrystals to desired sizes, could have application ence of various nonradiative energy-loss channels, the potential [11]. erbium luminescence intensity in a-Si : H : Er is still not high enough to make this material promising for appli- This report deals with a comparative study of the PL cation in light-emitting devices. spectra and kinetics of multilayered nc-Si/SiO2 struc- A promising approach to combating these difficul- tures, both erbium-doped and not containing this impu- ties could be the use of erbium-doped silicon nanocrys- rity, which makes it possible to judge the efficiency of tals (nc-Si) embedded in an insulating matrix [8Ð11]. It electronic excitation energy transfer from silicon should be pointed out that, although the wavelength of nanocrystals to the Er3+ ions in such structures.

HIGH-EFFICIENCY ERBIUM ION LUMINESCENCE 105

1.0 1 2 1 1 2 0.8 10–1 0.6 2 0.4 10–2

0.2 –3 PL intensity, arb. units PL intensity, arb. units 10 3 0 1.0 1.2 1.4 1.6 1.8 2.0 0.8 1.0 1.2 1.4 1.6 1.8 Photon energy, eV Photon energy, eV

Fig. 1. PL spectra of samples (1) A and (2) B measured at Fig. 2. PL spectra of samples (1) A, (2) AE, and (3) CE T = 300 K. obtained at T = 300 K.

2. SAMPLES AND EXPERIMENTAL spectral response of the system. The PL kinetics in the TECHNIQUES visible region of the spectrum was measured with a PM tube with a time constant of ~30 ns complemented by The nc-Si/SiO2 structures studied here were pre- an InGaAs photodiode with a time constant of ~1 µs to pared by successive deposition of SiO and SiO2 layers cover the IR region. Because the sensitivity of the latter on a c-Si substrate by reactive sputtering [10, 11]. The diode was not high enough, it was used in studies of the SiO layers were 2 and 3 nm thick in samples A and B, initial part of the kinetics only to measure the integrated respectively. The structures consisted of 40Ð50 pairs of PL intensity in the range 1.1Ð1.6 µm. The slow PL layers for a total thickness of 200Ð300 nm. The samples relaxation components were recorded using an InGaAs were thermally annealed at a temperature of 1100°C in photodiode with a time constant of 0.5 ms. The spectral a nitrogen environment for 60 min to produce layers of resolution in the measurement of the erbium PL kinet- closely packed Si nanocrystals separated by SiO2 layers ics was 4 nm. [11]. As follows from electron microscopy and x-ray Most of the studies of the PL spectra and kinetics ± diffraction measurements, the nanocrystal size was 2 were conducted in air at a temperature of 300 K. Sev- ± 0.5 and 3.5 0.5 nm in samples A and B, respectively. eral PL spectra were also measured in vacuum in the After the annealing, 300-keV Er3+ ions were implanted temperature range 10Ð450 K with the use of a DE-204N in part of the structures to a dose of 5 × 1014 cmÐ2. After closed-cycle cryostat (Advanced Research Systems). the implantation, the samples were thermally annealed at 950°C for 5 min. 3. RESULTS AND DISCUSSION Two lots of samples containing Si nanocrystals were Figure 1 shows PL spectra of samples A and B. The prepared in this way: the starting nc-Si/SiO2 structures (samples A and B) and Er-doped nc-Si/SiO : Er struc- A structures containing Si nanocrystals with smaller 2 average dimensions are seen to exhibit a blue-shifted tures (samples AE and BE). According to our estimates, PL spectrum. This shift is known [11, 12] to be usually the concentration of Er atoms in the AE and BE sam- associated with an increase in the band gap of nc-Si ples was approximately equal to that of Si nanocrystals, 19 Ð3 caused by the quantum-confinement effect. The PL which, from TEM observations, was ~10 cm [11]. spectra have a fairly large band width, with a FWHM of Besides the above structures, we also studied samples 0.35 eV for samples A and 0.3 eV for samples B. formed by implanting Er3+ ions of the above-mentioned energy and to the same dose into a uniform amorphous Our measurements revealed a weak increase (by a SiO film 250 nm thick, with its subsequent fast thermal factor 1.5Ð2) in the PL intensity of samples A and B 2 with the temperature decreasing from 300 to 6 K. Such annealing to remove implantation defects (CE sam- an increase indicates a good passivation of nonradiative ples). recombination centers in the structures under study. A pulsed N2 laser (photon energy 3.68 eV, pulse Note that the PL external quantum efficiency of sam- duration 10 ns, pulse energy density 10 µJ/cm2, pulse ples A at T = 10 K was found to be ~1%. Considering repetition frequency 100 Hz) was employed to excite the partial transparency of the structures to the pump the PL. The PL spectra were recorded using a comput- radiation (see below), this value appears fairly high. erized spectrometer equipped with an InGaAs photo- As is evident from Fig. 2, erbium implantation diode. The measured spectra were corrected for the results in a considerable suppression (by more than two

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

106 KASHKAROV et al. The band at 1.1 eV in the CE samples and the shoulder 1.0 10 K 1.0 observed in the same spectral region in the A and AE 60 K samples are apparently due to the penetration of the 0.8 300 K 0.5 pump radiation into the single-crystal silicon substrate 0 20 60 100 as a result of the layers under study being partially 0.6 103/T, K–1 transparent. 3+ 0.4 The data displayed in Fig. 2 indicate that Er ions in the nc-Si/SiO2 : Er structures under study are excited 0.2 through the transfer of electron excitation energy from

PL intensity, arb. units the Si nanocrystals. Recalling the relative magnitude of the PL intensities in samples A and AE, we can reason- 0 ably assume that the energy absorbed by the nanocrys- 0.76 0.78 0.80 0.82 0.84 0.86 tals is largely transferred to the optically active Er3+ Photon energy, eV ions. The actual mechanism of energy transfer will be discussed in more detail below. We note, however, that Fig. 3. PL spectra of sample BE measured in the Er3+ lumi- a certain contribution to the residual nc-Si PL in sam- nescence band at different temperatures. The inset shows ples AE and BE comes apparently from the nanocrys- the dependence of integrated erbium PL band intensity on tals that are so distant from Er3+ as to make their inter- reciprocal temperature. action with these ions inefﬁcient. As is evident from a comparison of curves 1 and 2, the nc-Si PL band undergoes a change in its spectral shape after the implanta- 3+ 100 tion of Er ions in the nc-Si/SiO2 structures. One clearly sees an enhancement of PL quenching by a few s

µ times with the photon energy increasing from 1.3 to ,

0 10

1 τ 1.7 eV. This can be interpreted, in terms of the mechanism of inhomogeneous broadening of the nc-Si PL 1 band, as indicating a more efficient energy transfer 1.5 1.7 1.9 10–1 hν, eV from smaller nanocrystals (i.e., nanocrystals with a larger band gap) [9]. In view of a possible contribution from homogeneous broadening associated with the 1 electronÐphonon coupling and polariton effects, this 10–2 PL intensity, arb. units increase in PL quenching with increasing photon 2 energy implies more efficient energy transfer from non- 3 thermalized excitons (i.e., excitons residing in nonsta- 0 100 200 300 400 tionary or excited states). µ Time, s Experiments showed that the erbium PL intensity in nc-Si/SiO : Er structures increases noticeably with the Fig. 4. PL kinetics of samples A obtained at various photon 2 energies: (1) 1.5, (2) 1.7, and (3) 1.9 eV. Symbols are exper- temperature decreasing from 300 to 10 K (Fig. 3). At imental data and solid lines represent fitting by an extended the same time, the band intensity integrated over the exponential. The inset shows the spectral response of the PL spectrum in the range 0.75Ð0.85 eV increases only by a relaxation times obtained by approximation for samples A factor of 1.5 (see inset to Fig. 3). Such an increase indi- (triangles) and AE (circles). cates a low efficiency of the competing nonradiative recombination channels, for instance, of the energy 3+ orders of magnitude) of the PL characteristic of the transfer from Er back to the solid matrix or of the undoped nc-Si samples and in the appearance of a recombination at point defects, such as silicon dangling strong band near 0.81 eV (λ = 1.535 µm). This band, bonds. 4 4 due to the intracenter I13/2 I15/2 transitions, is Let us turn now to an analysis of the PL kinetics of always observed in Er3+ ions embedded in a solid silicon nanocrystals. As seen from Fig. 4, relaxation of the PL intensity I (t) in undoped nc-Si/SiO structures matrix [1, 2]. Quenching of the nc-Si PL and formation PL 2 of the erbium band were also observed to occur in BE following a laser pulse cannot be fitted by an exponential. Our analysis showed that the PL kinetics can be structures with slightly larger nanocrystals. At the same well approximated by an extended exponential, time, the CE samples representing uniform a-SiO2 : Er3+ layers exhibited an extremely low PL intensity in () {}()τ β IPL t = I0 exp Ð t/ 0 , (1) the vicinity of 0.8 eV. These samples primarily pro- τ β duced a weak band at 1.1 eV, which originates from where 0 is the average time and is a parameter interband radiative recombination in the c-Si substrate. describing the deviation from exponential behavior.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 HIGH-EFFICIENCY ERBIUM ION LUMINESCENCE 107

The PL with the kinetics described by Eq. (1) is usu- 102 ally observed in disordered solid-state systems charac- 1 terized by a dispersion in the recombination times, for instance, in a-Si : H [5, 6] and porous silicon [13]. The 10 τ µ value of 0 was established to increase from 4 to 25 s with the photon energy decreasing from 2 to 1.5 eV (see 0.1 β 1 0 20 60 100 inset to Fig. 4). Note that the parameter remains prac- Time, µs tically unchanged and is close to 0.5. This behavior of τ β –1 0 and was observed in both A and B samples. More- 10 1 over, both samples revealed the same (within the experimental error and fitting accuracy) spectral response of PL intensity, arb. units –2 2 τ β 10 the quantities 0 and at the same PL photon energy. At the same time, erbium-doped structures exhibit a τ 0 2 4 6 8 10 decrease in 0 by a factor of about 2Ð2.5, whereas the value of β practically does not change. This effect was Time, ms observed in samples with nanocrystals of both sizes. Fig. 5. Er3+ PL kinetics for samples AE and BE (time reso- The observation that Er3+ implantation brings about lution 0.5 ms) obtained for photon energies of (1) 0.81 and quenching of the nc-Si PL intensity by two orders of (2) 0.84 eV. The inset shows the initial part of the kinetics magnitude (Fig. 2) while the relaxation times of the measured with a time resolution of 1 µs. Er3+ PL kinetics decrease only by one half compared to the times recorded for the undoped structures (Fig. 4) under study is direct energy transfer from excitons in a suggests the following explanation. It appears that the 3+ majority of Si nanocrystals in erbium-doped structures Si nanocrystal to Er ions, for instance, through the Förster mechanism [14]. The states excited in this pro- practically do not contribute to the luminescence in the 3+ range 1.2Ð1.9 eV. This may be due to the fact that such cess are the high-lying Er levels, which can be broad- nanocrystals have completely transferred the energy to ened substantially through electric-field fluctuations in the Er3+ ions, followed by luminescence at 0.81 eV. At the given solid matrix [1, 2]. Because the density of nanocrystals in the oxide matrix of the above structures the same time, the remaining nanocrystals (less than 19 Ð3 1%) have shorter PL times because of the interaction is quite high (~10 cm ) and, hence, the nanocrystals with the Er3+ ions. The times can also decrease, in prin- are separated by barriers only 1- to -3-nm thick, this ciple, as a result of nonradiative recombination on the mechanism of energy transfer from nanocrystals to the 3+ ions present in the matrix appears reasonable. This pro- defects produced by the Er implantation. The absence cess becomes still more probable in the cases where the of a noticeable thermal quenching of the PL in the sam- 3+ ples under study suggests, however, that the concentra- Er ion is localized directly at the nanocrystal surface. tion of such defects is low. The increase in the energy transfer efficiency for Figure 5 displays the PL relaxation kinetics of Er3+ nanocrystals of smaller size observed in our experi- ions measured for two luminescence photon energies, ments may be accounted for by a larger relative pene- 0.81 eV (i.e., at the band maximum) and 0.84 eV (at the tration of the exciton wave function into the oxide bar- short-wavelength side of the band). We readily see that rier, which has a finite height. The experimental data the erbium PL is characterized by a practically expo- can be readily interpreted if we assume that the time nential kinetics nearly independent of the photon required for the energy to be transferred from an exci- energy. Approximation of the kinetics by Eq. (1) yields ton to Er3+ is shorter than the exciton thermalization τ ≈ time. Estimation of the energy transfer time from the the average lifetime 0 3 ms. Such large values of the relaxation time are typical of the intrinsic radiative life- exciton to the ion made from the measured PL kinetics time of Er3+ ions; for instance, in the case of c-Si : Er, yields a value not in excess of a few microseconds. On they are observed only at liquid-helium temperature, the other hand, it is known that the thermalization time where the deexcitation processes are suppressed [1, 2]. of nonequilibrium carriers in semiconductor single crystals, which is determined by the electronÐphonon The initial part of the erbium PL kinetics measured with Ð12 Ð11 a microsecond-scale resolution is presented in the inset interaction processes, is on the order of 10 Ð10 s to Fig. 5. We readily see that the PL rise times of the [15]. Thermalization in a silicon nanocrystal can appar- Er3+ ions do not exceed 1Ð2 µs, which is shorter than ently be slowed down because of a decrease in the num- the nc-Si PL band relaxation times. This supports the ber of phonons, which is known to be proportional to above assumption of a high efficiency of energy trans- 3(N Ð 1), where N is the number of atoms. Note that a 3+ decrease in the spinÐlattice relaxation times by three to fer from nanocrystals to the Er ions. four orders of magnitude was observed to occur in Consider a possible mechanism of erbium PL exci- porous silicon with small nanocrystals [16]. The tation in nc-Si/SiO2 : Er structures in more detail. In our assumption of the exciton thermalization being slowed opinion, the most probable process in the samples down in silicon nanocrystals of a small size fits very

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 108 KASHKAROV et al. well with the increase in the energy transfer efficiency 2. K. Iga and S. Kinoshita, Progress in Technology for to the Er3+ ions observed to occur with decreasing Semiconductors Lasers (Springer, Berlin, 1996), Springer nanocrystal size. Ser. Mater. Sci., Vol. 30. 3. F. Priolo, G. Franzo, S. Coffa, et al., J. Appl. Phys. 78, 3874 (1995). 4. CONCLUSIONS 4. W. Fuhs, I. Ulber, G. Weiser, et al., Phys. Rev. B 56, 9545 (1997). To sum up, we have studied the luminescent proper- 5. E. A. Konstantinova, B. V. Kamenev, P. K. Kashkarov, 3+ ties of nc-Si/SiO2 multilayer structures containing Er et al., J. Non-Cryst. Solids 282 (2Ð3), 321 (2001). ions. It was shown that the energy absorbed in Si 6. B. V. Kamenev, V. Yu. Timoshenko, E. A. Konstantinova, nanocrystals can be transferred with a high efficiency to et al., J. Non-Cryst. Solids 299, 668 (2002). Er3+ ions, with its subsequent emission in the 1.5-µm 7. B. V. Kamenev, V. I. Emel’yanov, E. A. Konstantinova, region. We believe that the high efficiency of the erbium et al., Appl. Phys. B 74 (2), 151 (2002). PL excitation can be potentially applied in the develop- 8. A. J. Kenyon, C. E. Chryssou, C. W. Pitt, et al., J. Appl. ment of optical amplifiers and light-emitting devices in Phys. 91, 367 (2002). the 1.5-µm range. Further steps in optimizing the tech- 9. K. Watanabe, M. Fujii, and S. Hayashi, J. Appl. Phys. 90, 4761 (2001). nology for preparing nc-Si/SiO2 : Er structures, for instance, by increasing the number of layers and the 10. M. Schmidt, M. Zacharias, S. Richter, et al., Thin Solid Er3+ ion concentration, should apparently favor an Films 397, 211 (2001). increase in the erbium PL efficiency. 11. M. Zacharias, J. Heitmann, R. Shcholz, et al., Appl. Phys. Lett. 80, 661 (2002). 12. D. J. Lokwood, Z. H. Liu, and J. M. Baribeau, Phys. Rev. ACKNOWLEDGMENTS Lett. 76, 539 (1996). 13. A. G. Gullis, L. T. Canham, and P. D. J. Calcott, J. Appl. This study was supported by the CRDF (project no. Phys. 82, 909 (1997). RE2-2369), the Russian Foundation for Basic Research 14. V. M. Agranovich and M. D. Galanin, Electronic Excita- (project no. 02-02-17259), and programs of the Minis- tion Energy Transfer in Condensed Matter (Nauka, Mos- try of Industry, Science, and Technology of the Russian cow, 1978; North-Holland, Amsterdam, 1982). Federation. 15. S. A. Akhmanov, V. I. Emel’yanov, N. I. Koroteev, and V. I. Seminogov, Usp. Fiz. Nauk 147, 675 (1985) [Sov. Phys. Usp. 28, 1084 (1985)]. REFERENCES 16. E. A. Konstantinova, V. Yu. Timoshenko, and P. K. Kash- karov, Poverkhnost, No. 2, 32 (1996). 1. G. S. Pomrenke, P. B. Klein, and D. W. Langer, Rare Earth Doped Semiconductors (Pittsburgh, 1993), Mater. Res. Soc. Symp. Proc. MRS, Vol. 301. Translated by G. Skrebtsov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 109Ð112. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 110Ð113. Original Russian Text Copyright © 2004 by Shmagin, Remizov, Krasil’nik, Kuznetsov, Shabanov, Krasil’nikova, Kryzhkov, Drozdov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Effect of the pÐn Junction Breakdown Mechanism on the Er3+ Ion Electroluminescence Intensity and Excitation Efficiency in Si : Er Epitaxial Layers Grown through Sublimation Molecular Beam Epitaxy V. B. Shmagin, D. Yu. Remizov, Z. F. Krasil’nik, V. P. Kuznetsov, V. N. Shabanov, L. V. Krasil’nikova, D. I. Kryzhkov, and M. N. Drozdov Institute of the Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected]

Abstract—A series of Si : Er/Si light-emitting diode structures with a smoothly varying pÐn junction breakdown mechanism, grown through sublimation molecular-beam epitaxy, is used to investigate the effect of the breakdown mechanism on the electroluminescence of the structures. The maximal intensity and excitation efﬁ- ciency of room-temperature Er3+ ion electroluminescence are shown to be attained in diode structures with a mixed breakdown mechanism. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION breakdown mode. These structures were grown through sublimation molecular-beam epitaxy (SMBE) [8]. Photoluminescence (PL) and electroluminescence (EL) from Er3+ ions introduced into a single-crystal sil- 4 4 icon matrix ( I13/2 I15/2 transition in the 4f shell of 2. EXPERIMENTAL TECHNIQUE 3+ the Er ion) were first observed twenty years ago [1, 2]. The electroluminescent pp+nn+ diode structures Since then, noticeable advances have been made in the studied in this work were grown through SMBE on p-Si : technology for producing light-emitting Si : Er-based B substrates with (100) orientation and a resistivity of structures and in the study of the luminescence excita- 15 Ω cm. The n-Si : Er layer was about 1 µm thick, the tion and quenching mechanisms operating in these carrier concentration was varied from 3 × 1016 to structures. In particular, it has been established that, in 1 × 1018 cmÐ3, the growth temperature was ~520°C, and diode structures operating in the pÐn-junction break- × 18 Ð3 down mode at room temperature, impact EL excitation the Er concentration was ~1 10 cm . The light- 3+ emitting diodes were fabricated using the mesa tech- of Er ions is the most efficient mechanism [3]. Elec- 2 troluminescent pÐn diodes have been developed that nology. The mesa area was 2.5 mm , with 70% of this operate in the tunneling- [4] and avalanche breakdown area being transparent to the generated light. modes [5], and the Er3+ ion excitation cross sections The EL spectra were recorded in the range 1.0Ð µ have been determined to be 6 × 10Ð17 [6] and 2.3 × 1.6 m with a resolution of 6 nm by using an MDR-23 10−16 cm2 [7] for diodes operating in the tunneling- and grating monochromator and an infrared InGaAs photo- avalanche breakdown modes, respectively. detector cooled to liquid-nitrogen temperature. In order to excite and detect the EL spectra, we used pulsed However, in our opinion, the effect of the pÐn-junc- drive current modulation (pulse duration 4 ms, repetition breakdown mechanism (BM) on the character and tion frequency ~40 Hz, amplitude up to 500 mA) and excitation efficiency of the EL from Si : Er-based diode the conventional lock-in technique. The currentÐvolt- structures is still not clearly understood. In particular, it age (IÐU) characteristics of the diodes were measured has not been determined in what cases the tunneling- in the pulsed mode. The breakdown voltage Ub was and avalanche breakdown modes offer advantages over determined by extrapolating the linear portion of the IÐ each other and electroluminescent diodes in which a U curve at large reverse bias to its intersection with the mixed pÐn junction breakdown mechanism is operative voltage axis. have not been studied. In this work, using a series of light-emitting 3. EXPERIMENTAL RESULTS AND DISCUSSION Si : Er/Si diode structures with a smoothly varying BM as an example, we investigate the dependence of the The values of the breakdown voltage Ub for the radiative properties of a structure on the pÐn junction diode structures studied are listed in the table. By com-

110 SHMAGIN et al.

Diode breakdown voltages tures (including light-emitting Si : Er/Si structures) in which the epitaxial-layer thickness and the carrier con- Ub, V centration vary smoothly along the length of a structure Sample T = 300 K T = 77 K is described in [9]. Figure 1 shows the evolution of the EL spectra as 4A1 2.7 5.1 one goes from tunneling to avalanche diodes. In the 4A2 3.0 5.4 series of diodes in which the tunneling BM is dominant 4A3 3.5 5.6 (samples 4A1Ð3A0), the EL spectrum intensity as a whole increases, while the intensity ratio of the erbium 4A4 3.9 6.0 EL (the peak at wavelength 1.54 µm) and the hot EL 3A0 5.0 6.6 (wide band with a maximum at wavelength 1.2 µm) 3A1 6.8 7.1 remains unchanged as the breakdown voltage Ub 3A2 8.4 7.8 increases (Ub is assumed to have been measured at 3A3 11.1 9.6 room temperature unless otherwise speciﬁed). As Ub increases further (samples 3A1Ð3A3, in which the avalanche BM is dominant), the spectral radiation power paring the values of U measured at T = 300 and 77 K, density is redistributed: the erbium EL intensity b decreases, while the hot EL intensity increases. On the it can be seen that a smooth transition takes place from whole, the dependence of the erbium EL intensity on the tunneling (sample 4A1) to the avalanche BM (sam- the diode breakdown voltage is described by an asym- ple 3A3) in the series of diodes under study. We note metric bell-shaped curve (inset to Fig. 1), with the max- that all diode structures were grown in the same growth imum EL intensity reached in structures with Ub ~ 5 V, experiment. The technique used to grow epitaxial struc- which corresponds to a mixed pÐn-junction breakdown mechanism [10]. Now, we discuss the possible reasons for the decrease in the erbium EL intensity observed in 300 the diode structures for which the breakdown voltage is higher or lower than the value indicated above.

3.1. Structures in Which the Tunneling Breakdown ≤ Mechanism Is Dominant (Ub 5 V) It is well known that, in the case where the drive cur-

ELI, arb. units rent density is distributed uniformly over the pÐn junction area, the drive current-density dependence of the 400 0 Er3+ ion EL intensity is given by [3] 2 6 10 U , V jjÐ b στ------th q ELI ∝ ------, (1) jjÐ 1 + στ------th

ELI, arb. units q 3A3 where ELI is the EL intensity, j is the drive current density, j is the threshold drive current density, q is the ele- 3A2 th mentary charge, σ is the excitation cross section, and τ 3+ 3A1 is the lifetime of the optically active Er ion in the 4 στ excited state I13/2. The product is the characteristic 4A4 rate at which the EL intensity tends to saturation with increasing drive current density; therefore, this product 4A2 characterizes the efﬁciency of the EL excitation. 0 For all diodes in which the tunneling BM is domi- 1.0 1.2 1.4 1.6 nant (samples 4A1Ð3A0), the theoretical ELI( j) depen- λ, µm dence agrees well with the experimental data (Fig. 2a); therefore, Eq. (1) adequately describes the Er3+ ion Fig. 1. Electroluminescence spectra of Si : Er/Si diode excitation and relaxation in tunneling diodes. As the structures at T = 300 K for a drive current density of στ 2 breakdown voltage increases, the quantity increases 8 A/cm . For the sake of convenience, the spectra are smoothly (inset to Fig. 2a) from 1.4 × 10Ð20 cm2 s for shifted along the abscissa and ordinate axes. The inset × Ð20 2 shows the dependence of the Er3+ ion EL intensity on diode Ub = 2.7 V to 9.4 10 cm s for Ub = 5.0 V; this breakdown voltage for ﬁxed current density. increase is likely due to the fact that the electron gas is

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 EFFECT OF THE PÐN JUNCTION BREAKDOWN MECHANISM 111

12 s 2

cm 8 (a) (b) –20

, 10 0.2 στ 4 400

0 2 4 6 Ub, V ELI, arb. units ELI, arb. units

4A1 4A3 3A0

0 2 4 6 8 0 0.08 0.16 j, A/cm2 I, A

Fig. 2. Dependence of the erbium EL intensity (a) on drive current density and (b) on drive current for diode structures in which (a) the tunneling- or (b) avalanche breakdown mechanism is dominant. The inset shows the dependence of the quantity στ on breakdown voltage for tunneling diodes. (b) Dashed and dotted lines represent the contributions from the two terms in Eq. (2) to the experimental ELI(I) dependence.

≥ heated with increasing breakdown voltage of an elec- diodes 3A2 and 3A3 (Ub 8.4 V), the pÐn junction troluminescent diode. breakdown is highly nonuniform; a large number of Analysis of the data presented in Fig. 2a shows that, microplasma spots (about one hundred) are observed at a fixed value of the drive current density, the EL on the radiating surface of the pÐn junction in the intensity is lower in samples with lower EL excitation breakdown regime (Fig. 3c). In the microplasma break- efficiency (with smaller values of στ) and that the down regime, the drive current flows primarily through decrease in the Er3+ ion EL intensity in tunneling diodes microplasma filaments; therefore, in the greater part of with low values of the breakdown voltage (left-hand the space-charge region where there are no microplasmas, the Er3+ ion excitation efficiency drops, which branch of the ELI(Ub) curve in the inset to Fig. 1) is due to a decrease in the EL excitation efficiency. causes the integrated erbium EL intensity to decrease. In our opinion, the significant decrease in the Er3+ EL intensity observed in samples 3A2 and 3A3, in which 3.2. Structures in Which the Avalanche Breakdown the avalanche BM is dominant (the right-hand branch ≥ Mechanism Is Dominant (Ub 7 V) of the ELI(Ub) curve in the inset to Fig. 1), is due to the We correlated the changes in the EL spectra of diode pÐn junction breakdown being nonuniform in these ≥ samples and, accordingly, to the nonuniform drive cur- structures with Ub 7 V (Fig. 1) with the changes in light emission of the diodes in the visible part of the rent density distribution over the pÐn junction area. We spectrum; this emission was observed under diode note that the formation of microplasmas is characteris- breakdown conditions with the help of an MBS-10 tic of avalanche pÐn junction breakdown in silicon [11]. ≤ microscope (Fig. 3). In samples 4A1Ð3A0 (Ub 5 V), The nonuniform drive current density distribution the light emission is uniform over the portion of the pÐ over the pÐn junction area in diode structures with n junction area not covered with a metal (Fig. 3a) and developed microplasma breakdown manifests itself in its intensity increases with the breakdown voltage. Iso- the ELI(I) dependence, where I is the drive current (Fig. lated bright spots (microplasmas [11]) are observed on 2b). The ELI(I) dependence for samples 3A2 and 3A3 ≈ the surface of sample 3A1 (Ub 6.8 V; Fig. 3b). In can be described adequately under the assumption that

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 112 SHMAGIN et al.

(a) (b) (c)

Fig. 3. Photographs of the emission from Si : Er/Si diode structures in the visible part of the spectrum under pÐn junction breakdown conditions: samples (a) 4A4, (b) 3A1, and (c) 3A3. the drive current density distribution over the pÐn junc- mixed-breakdown conditions are preferable, because a tion area is nonuniform in these samples. compromise is reached in them between, on the one 3+ Indeed, let us assume that the pÐn junction area con- hand, the high Er ion EL intensity and excitation effi- sists of two regions within each of which the drive cur- ciency and, on the other, the uniform character of the pÐ rent density distribution is uniform. Each of these n junction breakdown. regions is characterized by conductance Gi, area Ai, and th threshold drive current density ji . In this case, the ACKNOWLEDGMENTS dependence of the Er3+ ion EL intensity on the total This study was supported by the Russian Founda- drive current I is given by tion for Basic Research (project no. 02-02-16773) and the Ministry of Industry, Science, and Technology στG I th ------1 ------Ð j (State contract no. 40.020.1.1.1159). q G + G A 1 ELI ∝ A ------1 2 1 1 στ G1 I th REFERENCES 1 + ------------Ð j1 q G1 + G2 A1 1. H. Ennen, J. Schneider, G. Pomrenke, and A. Axmann, (2) Appl. Phys. Lett. 43, 943 (1983). στG2 I th ------------Ð j2 2. H. Ennen, G. Pomrenke, A. Axmann, et al., Appl. Phys. q G1 + G2 A2 Lett. 46, 381 (1985). + A2------. στG I th ------2 ------3. G. Franzo, S. Coffa, F. Priolo, and C. Spinella, J. Appl. 1 + Ð j2 Phys. 81, 2784 (1997). q G1 + G2 A2 4. G. Franzo, F. Priolo, S. Coffa, et al., Appl. Phys. Lett. 64, It can be seen from Fig. 2b that the ELI(I) dependence 2235 (1994). for sample 3A2 (avalanche diode) is described ade- 5. N. A. Sobolev, A. M. Emel’yanov, and K. F. Shtel’makh, quately by Eq. (2), which confirms our assumption that Appl. Phys. Lett. 71, 1930 (1997). the erbium ion excitation is nonuniform in structures in 6. S. Coffa, G. Franzo, and F. Priolo, Appl. Phys. Lett. 69, which the avalanche BM is dominant. 2077 (1996). 7. N. A. Sobolev, Yu. A. Nikolaev, A. M. Emel’yanov, et al., 4. CONCLUSIONS J. Lumin. 80, 315 (1999). 8. V. P. Kuznetsov and R. A. Rubtsova, Fiz. Tekh. Polupro- Thus, we have investigated the electroluminescence vodn. (St. Petersburg) 34, 519 (2000) [Semiconductors from Si : Er/Si diode structures emitted under pÐn junc- 34, 502 (2000)]. tion breakdown conditions. For diodes in which the 3+ 9. E. N. Morozova, V. B. Shmagin, Z. F. Krasil’nik, et al., avalanche BM is dominant or nearly dominant, the Er Izv. Ross. Akad. Nauk, Ser. Fiz. 67, 283 (2003). ion excitation efficiency has been shown to be an order 10. S. Sze, Physics of Semiconductor Devices, 2nd ed. of magnitude higher than that for tunneling diodes. (Wiley, New York, 1981; Mir, Moscow, 1984), Chap. 1. However, as the avalanche breakdown becomes more pronounced, the drive current density distribution over 11. I. V. Grekhov and Yu. N. Serezhkin, Avalanche Break- down of pÐn Junctions in Semiconductors (Énergiya, the pÐn junction area becomes highly nonuniform Leningrad, 1980). (microplasma breakdown), with the consequence that the Er3+ ion EL intensity decreases noticeably. In our opinion, the electroluminescent diodes operating under Translated by Yu. Epifanov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 113Ð117. From Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 114Ð118. Original English Text Copyright © 2004 by Stepikhova, Cerqueira, Losurdo, Giangregorio, Alves, Monteiro, Soares.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) The Role of Microstructure in Luminescent Properties of Er-doped Nanocrystalline Si Thin Films* M. V. Stepikhova1, M. F. Cerqueira2, M. Losurdo3, M. M. Giangregorio3, E. Alves4, T. Monteiro5, and M. J. Soares5 1 Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia 2 Departamento de Física, Universidade do Minho, Campus de Gualtar, Braga, 4710-057 Portugal 3 Institute of Inorganic Methodologies and Plasmas, IMIP-CNR, via Orabona, Bari, 4-70126 Italy 4 Instituto Técnico Nuclear ITN, EN 10, Sacavém, 2686-953 Portugal 5 Departamento de Física, Universidade de Aveiro, Campus de Santiago, Aveiro, 3700 Portugal

Abstract—In this contribution, we present a structural and photoluminescence (PL) analysis of Er-doped nanocrystalline silicon thin films produced by rf magnetron sputtering method. We show the strong influence of the presence of nanocrystalline fraction in films on their luminescence efficiency at 1.54 µm studied on a series of specially prepared samples with different crystallinity, i.e., percentage and sizes of Si nanocrystals. A strong increase, by about two orders of magnitude, of Er-related PL intensity in these samples with lowering of the Si nanocrystal sizes from 7.9 to about 1.5 nm is observed. The results are discussed in terms of the sensitization effect of Si nanocrystals on Er ions. © 2004 MAIK “Nauka/Interperiodica”.

* 1. INTRODUCTION attractive for device applications. One can show that the presence of a crystalline fraction in thin films results in Recently, Er-doped Si materials were widely stud- an increase in film conductivity of several orders of ied in context with the interest in temperature-stable magnitude [6]. Er-doped nc-Si : H films with well- light emitters for optical communication systems. The defined crystallinity and nanocrystal sizes (varied from intra-4f-shell transitions between the two lowest spin- 1Ð3 to 8 nm) were deposited and studied in both the orbit levels of Er3+ ions, namely, the transitions near-IR (1.54 µm) and visible luminescence ranges. 4 4 µ I13/2 I15/2, occur at 1.54 m, a wavelength close to The results are discussed in terms of the role of Si that with minimum loss in silica-based optical fibers. nanocrystallites in the luminescent properties of films. The realization of electroluminescence devices on the basis of Si : Er has been reported [1Ð3]. Nevertheless, the main drawback to using a bulk Si crystal as a host 2. EXPERIMENTAL for Er3+ is the strong temperature quenching of 1.54 µm Erbium-doped nanocrystalline silicon thin films luminescence. It appears that this situation may be con- were grown by rf magnetron sputtering in an Ar/H2 siderably improved by the incorporation of Er ions in atmosphere on ordinary glass substrates. The procedure nanocrystal-containing materials. The idea is based on applied was similar to that used for the preparation of the band-gap widening of nanometer-size Si, which undoped µc-Si : H films in [7], only modified by the consequently has to result in reducing the thermal introduction of small pieces of metallic erbium to the c- quenching for Er luminescence. Moreover, Si nanoc- Si target for Er doping. The target used was c-Si of high rystals that are well known to emit in the visible range purity (99.99%). The erbium was placed in a low ero- (due to the recombination of confined excitons within sion area on the silicon target in order to keep a moder- the nanostructures) may act as efficient sensitizers for ate rate of Er impurity. The substrateÐtarget distance rare earth ions [4, 5]. was fixed at 55 mm. In this contribution, we discuss the luminescent Samples with different structural parameters, i.e., properties of Er-doped nanocrystalline silicon thin different crystalline fraction and grain sizes, were films (nc-Si : Er) produced by the rf reactive magnetron obtained by varying the experimental parameters (RF sputtering method. The advantages of these films, when power, temperature, Er content, and gas-mixture com- compared with the intensively studied nanocrystal-con- position). In particular, amorphous films (see Er28) were obtained at low hydrogen dilution, i.e., a low R taining SiO2 structures and a-Si : H,O,Er films, is their H relatively high conductivity, which makes the material value (see Table 1). Nanocrystalline samples were grown in a H2-rich atmosphere, where the role of *This article was submitted by the authors in English. atomic hydrogen is to etch preferentially the amor-

114 STEPIKHOVA et al.

Table 1. Growth conditions for erbium-doped nanocrystal- measurements in the near-IR range were performed line silicon thin films with a Bruker 66V Fourier-transform spectrometer. The ° signal was detected with a North-Coast EO-817 liquid Sample Temperature, C RF power, W RH nitrogenÐcooled germanium detector. The 514.5-nm Er22 400 80 0.63 line of an Ar laser was used for the excitation. PL stud- Er19 200 80 0.63 ies in the visible spectral range were carried out under excitation with a 325-nm line of a cw HeÐCd laser with Er24 50 80 0.63 a Spex 1704 monochromator and a cooled Hamamatsu Er28 200 150 0.37 R928 photomultiplier in the detection chain. Er33 25 80 0.63 Note: R = pH /(pH + pAr) is the hydrogen fraction. H 2 2 3. RESULTS AND DISCUSSION Figure 1 shows the XRD and Raman spectra for the phous phase and promote the amorphous-to-crystalline nc-Si : Er samples studied. The broad band related to transition. The growth conditions of the films are listed the silicon amorphous matrix is present in the spectra in Table 1. for all samples. The Er28 sample grown at higher RF The chemical composition of the films was deter- power but in an Ar-rich atmosphere does not show any mined using Rutherford backscattering spectroscopy crystalline peak in either the XRD or Raman spectra and elastic recoil detection techniques. The structural (the same behavior was also observed for the Er33 sam- characterization was performed using standard micro- ple). In contrast, the (111), (220), and (311) diffraction Raman spectroscopy under excitation with the peaks of c-Si are visible for all other samples. The 514.5-nm Ar+ laser line and by x-ray diffractometry in peaks are well evident for the Er22 sample grown at ° the grazing incidence geometry. For more detailed high H2 dilution and a high temperature of 400 C, both analysis of the microstructure and film “anatomy,” parameters promoting the amorphous-to-crystalline high-resolution transmission electron microscopy transition. The diffraction peaks have a lower intensity (HRTEM) and spectroscopic ellipsometry (SE) were for the Er19 and Er24 samples, indicating a decrease in applied. SE spectra of the pseudodielectric function, the crystallinity and/or the crystallite grain size, which 〈ε〉 〈ε 〉 〈ε 〉 = 1 + i 2 , were acquired in the 1.5- to 5.5-eV is also confirmed by the intensity ratio of the Stokes energy range by using a phase-modulated spectro- peaks at 480 cmÐ1 (a-Si related) and at 520 cmÐ1 (trans- scopic ellipsometer (UVISEL-Jobin Yvon) at an inci- verse optical (TO) mode of c-Si) in the Raman spectra dent angle of 70.5°. SE spectra were analyzed in terms (Fig. 1b). The diffraction peak analysis, by fitting a of optical models based on the Bruggeman effective pseudo-Voigt function to the (111) c-Si diffraction peak medium approximation (for more details, see [8]). The [7], gives the average crystal size for the Si nanocrys- thickness of the films was evaluated from analysis of tals presented in Table 2. In the same table, the data of the interference pattern in transmission spectra making Raman spectroscopy are also presented. To analyze the use of the Swanepoel method [9] and from the spectro- Raman spectra, the TO replica of amorphous structure scopic ellipsometry data. Photoluminescence (PL) has been approximated by a Gaussian profile and the

Intensity, arb. units Intensity, arb. units 100 (a) (b) 113 90 (111) 80 70 108 (220) 60 Er19 (311) 103 50 Er22 Er22 40 98 30 Er28 20 Er24 Er24 93 Er28 10 Er19 0 88 20 40 60 80 300 400 500 600 2Θ, deg Raman shift, cm–1

Fig. 1. (a) XRD and (b) Raman spectra of nc-Si : Er thin ﬁlms.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

THE ROLE OF MICROSTRUCTURE IN LUMINESCENT PROPERTIES 115

Table 2. Content of elements, thickness, and structural parameters of nc-Si : Er samples

Sample Er, % Si, % O, % H, % d, nm DX, nm DR, nm CR, % SE data Er22 0.10 71.7 8.8 17.6 2089 7.0 7.9 65 87% µc-Si Er19 0.12 62 34 23 483 5.7 6.5 43 31% µc-Si Er24 0.17 56.5 17.6 25.4 538 3.9 5.5 23 25% µc-Si Er28 0.11 60.9 2.9 34.3 1295 Ð Ð 0 10% nc-Si Er33 0.02 73.4 <1 25.8 1499 Ð Ð 0 38% nc-Si

Note: D — average crystal size, R — Raman spectroscopy, X — XRD analysis, CR — crystalline volume fraction determined by Raman spectroscopy, d — film thickness. crystalline response analysis was performed on the with a maximum at 6500 cmÐ1 and a characteristic basis of the strong phonon confinement model [10]. shoulder at around 6457 cmÐ1, like for Er in glasslike and amorphous materials [11], the Er-related spectrum Near-IR photoluminescence spectra measured at transforms in highly crystalline films (sample Er22) in 77 K in nc-Si : Er samples are shown in Fig. 2. Let us the spectrum with a fine line structure (see inset A in consider the highly crystalline samples according to Fig. 2), giving evidence for the incorporation of Er ions XRD and Raman data (samples Er24, Er19, and Er22 in regular crystalline surroundings. At the same time, in with nanocrystal sizes of 5.5Ð7.9 nm and crystallinity the spectra of highly crystalline samples, the lines at CR = 23Ð65%). The spectra of these samples show a 7500 and 9435 cmÐ1 appear and increase with the crys- luminescence peak at 1.54 µm related to the intraatomic tallinity and could be assigned following from their 4 4 3+ ( I13/2 I15/2) transitions of Er ions. Being rela- energetic position as the defectlike and excitonic tran- tively broad in a low crystalline sample (sample Er24) sitions in Si crystallites. However, one can see that the

1.1 Er33 T = 77 K Dnc < 3 nm Dnc, nm (×0.2) 5.5 6.5 7.5 1.0 6 0.10 Er22 6506 B 0.9 Er28 A 5 (×0.2) 0.08 6474 0.8 4 0.06 6447 3 0.7 0.04 2 1 0.6 0.02

PL intensity, arb. units 0 0.5 Er24 6300 6400 6500 6600 10 30 20 40 60 –1 Wavenumber, cm Er related PL intensity, arb. units nc fraction, % C , % 0.4 R PL intensity, arb. units 0.3 Er19 1.17 eV 0.2 Er22 0.93 eV 0.1 0 6000 6500 7000 7500 8000 8500 9000 9500 Wavenumber, cm–1

Fig. 2. PL spectra of nc-Si : Er samples with different contents of the crystalline fraction. Insets show (A) the enlarged Er-related region in the PL spectrum for sample Er22 and (B) the correlation between the PL intensity (Er-related peak) and the presence of a crystalline fraction in nc-Si : Er samples. The right part of inset B shows the situation for highly crystalline samples according to XRD and Raman analysis (the CR and DR values on the bottom and top axes correspond to the Raman data). On the left part of inset B, PL intensities for the samples with a nanocrystallite fraction with 1Ð3 nm crystallite grain sizes are presented, where the values for the nc fraction are taken from SE data. The luminescence intensities at 1.54 µm in this inset are normalized to the thickness of the ﬁlms.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

116 STEPIKHOVA et al.

101 in them reduces by more than an order of magnitude with an increase in the crystalline fraction from 23 to Er33 65% (and crystallite size from 5.5 to 7.9 nm; see inset B in Fig. 2). The most intense Er-related PL was observed in low Er28 crystalline samples determined as “amorphous” according to the Raman and XRD analysis (samples Er28 and Er33 in Table 2). In particular, the PL inten- 1.2 sity of the Er33 sample exceeds that for highly crystal- Er33 T = 300 K 1.0 line sample Er22 by about two orders of magnitude (see 170 meV inset to Fig. 2) despite the lower Er content. These sam- 0.8 ples show strong luminescence at room temperature Er28 (Fig. 3). The PL intensity decreases only ﬁvefold when 0.6 going from 77 to 300 K with deactivation energies of 100 PL intensity, arb. units 154 and 170 meV. 0.4

154 meV It seems that it would be difﬁcult to explain this dra- 0.2

PL intensity, arb. units matic increase in luminescent efficiency arising upon 0 the transition from crystalline to amorphous film structure even because of the strong difference in the excita- 5500 6500 7500 Wavenumber, cm–1 tion cross sections for Er ions in these two matrices. It is known that the excitation cross section for the direct 468101214 excitation of Er ions in amorphous matrices is about 1000/T, K–1 five orders of magnitude less than that for Er in crystalline Si (8 × 10Ð21 and 3 × 10Ð15 cm2, respectively [12, Fig. 3. Temperature dependences of Er-related PL intensity 13]). Of course, one cannot exclude the role of nonradi- obtained in nc-Si : Er thin films (samples Er28 and Er33). ative recombination channels in these composite struc- The solid lines are exponential fits of experimental data with deactivation energies of 170 and 154 meV for samples tures. So, we can image that the enlargement of the Er33 and Er28, respectively. The inset shows PL spectra of crystalline fraction will enhance the nanocrystalline the samples at room temperature. interactions in films and, therefore, the probability of excitons propagating in the crystalline network and recombining nonradiatively. However, in fact, we did increase of crystallinity in these samples results in a not observe any direct evidence of a strong influence of strong quenching of Er-related photoluminescence. nonradiative processes on the luminescent efficiency of Though the samples have a similar Er atomic percent- the films. There is no strong correlation between the age (0.1Ð0.17%, as estimated by RBS), the PL intensity amount of hydrogen in the films and their luminescent

Er33 (a) (b)

Er22

SiO2 3 nm Er33 55% µc-Si + 21% SiO 229 nm SiO 3 nm 24% a-Si + 0.3% Er 2 µ 87% c-Si + 12% SiO 732 nm 38% nc-Si + 29% voids 1496 nm 0.3%Er 33% a-Si : H + 0.2% Er µ 96% c-Si + 6% SiO 1125 nm Glass 0.3%Er χ2 = 0.28 Glass 2 5 nm χ = 0.27

Fig. 4. (a) HRTEM image obtained for sample Er33 and (b) structural models of samples Er33 and Er22 derived from SE analysis.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 THE ROLE OF MICROSTRUCTURE IN LUMINESCENT PROPERTIES 117 properties (as a rule, hydrogen passivates the dangling structural properties. The nc-Si : Er films with well- bonds in amorphous/crystalline tissue, thus intensify- defined crystallinity and nanocrystal sizes (varied from ing PL).We observed even the opposite, an increase in 1Ð3 to 8 nm) were deposited and studied in both the the film PL intensity after annealing at 500°C for 5 h; near-IR and visible luminescence ranges. A strong this procedure depletes the material with hydrogen. influence of Si nanocrystals on the luminescent proper- Moreover, the presence of oxygen in films, an element ties of the films at 1.54 µm has been observed, where known as an “activator” for Er ions, also does not influ- the most intense Er photoluminescence obtained relates ence noticeably the film luminescence (see Table 2). to the low crystalline films with nanocrystal grain sizes less than 3 nm. These films demonstrated intense One can assume that the luminescence of Er ions in µ “amorphous” samples is activated by the nanocrystals 1.54- m luminescence at room temperature with a tem- with very small grain sizes (<3 nm). The first indication perature-quenching coefficient (in the range 77–300 K) of the presence of these nanocrystals in films was of only about 5. The results have been explained in obtained in spectroscopic ellipsometry studies. SE data terms of the sensitization effect of Si nanocrystals on Er predict the presence of small nanocrystals in samples rare-earth ions. Er28 and Er33 in an amount of 10 and 38%, respectively (SE analysis of the nc-Si thin films with small ACKNOWLEDGMENTS nanocrystal grain sizes were discussed in detail in [14]; see also the models in Fig. 4b). Indeed, this prediction This work was partially supported by the FCT foun- can be confirmed by HRTEM measurements. A cross- dation (Portugal) and the Russian Foundation for Basic sectional HRTEM image obtained for the Er33 sample Research (project no. 01-02-16439). is presented in Fig. 4a. The micrograph shows that the matrix of the a-Si : H films contains a high density of REFERENCES small clusters, which were identified on the basis of 1. Silicon-Based Optoelectronics, Ed. by S. Coffa and electron diffraction analysis as silicon nanocrystals. L. Tsybeskov, MRS Bull., No. 23, 16 (1998). The lattice fringes corresponding to the (111) planes of 2. J. Stimmer, A. Reittinger, J. F. Nützel, et al., Appl. Phys. silicon are visible in the figure. Statistical analysis of Lett. 68, 3290 (1996). the nanocrystallite size distribution gives a nanocrystal 3. B. Andreev, V. Chalkov, O. Gusev, et al., Nanotechnol- mean radius of about 1.5 nm for this sample. Note a PL ogy 13, 97 (2002). response in the visible range at around 700Ð720 nm was 4. P. G. Kik and A. Polman, Mater. Sci. Eng. B 81 (1Ð3), 3 also detected in these samples. We believe that, in our (2001). case, the situation is similar to that observed by Fujii et 5. F. Priolo, G. Franzo, F. Iacona, et al., Mater. Sci. Eng. B al. [15], who studied the correlation between the Er- 81 (1Ð3), 9 (2001). related PL intensity and the nc-Si grain sizes in nc-Si- 6. M. F. Cerqueira, J. A. Ferreira, and G. J. Adriaenssens, containing SiO2 films doped with Er. These authors Thin Solid Films 370, 128 (2000). obtained a strong, by about two orders of magnitude, 7. M. F. Cerqueira, M. Andritschky, L. Rebouta, et al., Vac- increase in the Er PL intensity with lowering the nc-Si uum 46, 1385 (1995). grain size from 3.8 to 2.7 nm. Actually, starting with 8. M. Losurdo, M. F. Cerqueira, E. Alves, et al., Physica E these sizes, one can speak about a remarkable band-gap (Amsterdam) 16, 414 (2003). widening and the role of quantum size effects in Si [16]. 9. R. Swanepoel, J. Phys. E 16, 1214 (1998). Therefore, one can conclude that the seemingly strange 10. I. H. Campbell and P. M. Fauchet, Solid State Commun. increase in PL intensity in our “amorphous samples” 58, 739 (1986). can also be understood as a result of the sensitizing 11. M. Stepikhova, W. Jantsch, G. Kocher, et al., Appl. Phys. effect of Si nanocrystals on Er ions related to the Lett. 71, 2975 (1997). enhancement of the excitation probability for the last 12. G. N. van Hoven, J. H. Shin, A. Polman, et al., J. Appl. ones due to the recombination of electronÐhole pairs Phys. 78, 2642 (1995). confined in nanocrystals. 13. G. Franzo, V. Vinciguerra, and F. Priolo, Appl. Phys. A 69, 3 (1999). 4. SUMMARY 14. M. Losurdo, M. M. Giangregorio, P. Capezzuto, et al., Appl. Phys. Lett. (2003) (in press). In this contribution, we have demonstrated the pos- 15. M. Fujii, M. Yoshida, S. Hayashi, and K. Yamamoto, sibility of producing, by the reactive magnetron sputter- J. Appl. Phys. 84, 4525 (1998). ing method, effectively emitting nc-Si : H thin films 16. T. Takagahara and K. Takeda, Phys. Rev. B 46 (23), doped with Er and have discussed their luminescent and 15578 (1992).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 118Ð121. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 119Ð122. Original Russian Text Copyright © 2004 by Vorob’ev, Panevin, Fedosov, Firsov, Shalygin, Hanna, Seilmeier, Moumanis, Julien, Zhukov, Ustinov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Intraband Absorption and Emission of Light in Quantum Wells and Quantum Dots L. E. Vorob’ev*, V. Yu. Panevin*, N. K. Fedosov*, D. A. Firsov*, V. A. Shalygin*, S. Hanna**, A. Seilmeier**, Kh. Moumanis***, F. Julien***, A. E. Zhukov****, and V. M. Ustinov**** *St. Petersburg State Technical University, Politekhnicheskaya ul. 29, St. Petersburg, 195251 Russia e-mail: [email protected] **Physikalisches Institut, Universität Bayreuth, Bayreuth, 95440 Germany ***Institut d’Electronique Fondamentale, Université Paris-Sud, Orsay, 91405 France ****Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia

Abstract—High-resolution spectroscopy in the mid-infrared spectral range is used to study electronic transitions between size-quantization subbands in stepped quantum wells under picosecond interband excitation. The contributions from intersubband and intrasubband absorption of light are separated by using the difference in time proﬁles of the absorption coefﬁcient for these cases. For stepped quantum wells, spontaneous interband luminescence and superluminescence are studied for different excitation levels. For structures with quantum dots, the intraband absorption spectra for n- and p-type structures and the spectra of photoinduced intraband absorption and emission (for polarized radiation) for undoped structures are studied. © 2004 MAIK “Nauka/Interperiodica”.

For semiconductor nanostructures with quantum 1. INTRABAND LIGHT ABSORPTION dots (QDs) and stepped quantum wells (QWs), the pop- IN QUANTUM WELLS: ulation inversion between size-quantization levels or HIGH-RESOLUTION STUDIES subbands is possible when electrons and holes are injected. We propose a scheme of a laser in the mid-IR We studied structures consisting of 35 layers of region based on intraband electron transitions in three- undoped GaAs/AlxGa1 Ð xAs quantum wells separated level, stepped QWs or in QDs [1]. A metastable level, by 20-nm-thick barriers. The potential proﬁle of a sin- which is necessary for the population inversion, is gle QW is shown in the inset to Fig. 1a. Nonequilibrium formed in QWs due to a specially chosen potential pro- electrons are excited in a structure by using a high- power pumping Nd : YLF laser (λ = 523.5 nm, ∆t = ﬁle ensuring weak overlap of the wave functions of λ µ interacting levels and weakening of scattering by opti- 4 ps). Probe mid-IR radiation pulses ( = 4Ð18 m), synchronized with pump pulses, are formed by a non- cal phonons; in QDs, a metastable level results from the linear element. The measurements are performed at T = phonon bottleneck effect. To construct such a laser, 300 K. studies of the charge carrier energy distributions and of the electron lifetimes and relaxation mechanisms in In Fig. 1 we show the measured changes in intra- QDs and QWs are needed. band absorption for different frequencies of pump radiation and different time shifts of the probing pulse with In this work, we studied different optical phenom- respect to the pump pulse. The observed light-induced ena observed under optical interband excitation of non- absorption contains contributions both from intersub- equilibrium eÐh pairs in stepped InGaAs/AlGaAs QWs band transitions and from intrasubband absorption by and in InAs/GaAs QDs. In particular, we studied inter- free electrons. The position of the absorption band band photoluminescence (PL) at high excitation levels, observed at បω = 99 meV is close to the theoretical including time-resolved PL in the picosecond range, value of 111.6 meV for the e2Ðe3 transition. This dif- superluminescence, and intraband absorption and intra- ference can be attributed to the deviation of the actual band spontaneous emission of radiation in the mid-IR parameters of the structure from the calculated values range. and to the effect of many-particle interactions on the

INTRABAND ABSORPTION AND EMISSION OF LIGHT 119

300 (‡) e2 hh2 (a) e →e e3 200 2 3 111.6 meV 0.16 8 e1→hh1 1 Barrier e2 2 100 e1 , arb. units 0.14 3 Energy, meV 0 ∆α 0.12 6 → 30 40 50 60 70 e3 hh5 0.10 z, nm 0.08 4 → Pump–probe e1→lh1 e3 hh3 0.06 delay time, ps: 14.7 0.04 2

111 PL intensity, arb. units 0.02

Absorption change 96 98 100 102 104 106 0 Probe photon energy, meV 1.3 1.4 1.5 1.6 1.7 1.8 1.9 (b) Energy, eV (b) បω probe = 99 meV → 0.20 បω e3 hh5 pump = 2.37 eV e1→hh1 e2→hh2 Barrier 0.16 80 →

, arb. units e1 lh1

∆α 0.12 60 0.08 1 2 × 0.04 40 70 បω e3 hh3 0 probe = 104 meV –0.04 20 PL intensity, arb. units

Absorption change –60 –200 20 60 100 140 160 Pump–probe delay time, ps 0 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Fig. 1. (a) Spectra of absorption change for QWs for differ- Energy, eV ent delay times and (b) the dynamics of the absorption for different frequencies of pump radiation. Transitions are Fig. 2. (a) Surface PL spectra. The distance between the schematically shown in the inset. lens (the focal distance 100 mm) and the sample surface is (1) 125, (2) 105, and (3) 100 mm. The arrows indicate the calculated values of the interband transition energies. (b) PL spectra for radiation from the end side of the structure. The energy spectrum; this effect was neglected in our calcu- pump-pulse energies are (1) 0.062 and (2) 4.5 µJ. Excitation lations. area is 0.075 × 3 mm. The arrows indicate the calculated The pumping level corresponded to the surface den- values of the interband-transition energies. sities of nonequilibrium electrons exceeding 5 × 1012 cmÐ2 per QW. For such a high excitation level, not ing the absorption coefficient for transitions e2Ðe3. only the lowest subband e1 but also the excited states e2 Intrasubband absorption due to free electrons outside and e3 are filled; therefore, one can observe intersub- the band of e2Ðe3 transitions involves electron scatter- band absorption corresponding to the e2Ðe3 transitions. ing by equilibrium and nonequilibrium LO phonons. Intersubband absorption at the center of the band After the end of the pump pulse, the absorption is rather បω បω ( probe = 99 meV) and outside the band ( probe = large, but then it decreases due to a decrease in electron 104 meV) has different time profiles. Absorption at the temperature and in the number of nonequilibrium center of the band increases in time after the end of a phonons. pump pulse, whereas the absorption outside the band, By analyzing the data obtained, we can find the on the contrary, decreases. These effects can be electron cooling time; when this time is long, it is deter- explained by strong heating of the electron gas during a mined by the lifetime of nonequilibrium LO phonons; pump pulse. A high pumping level and the high photon if the cooling time is short, it is dictated by the phonon energy of pump radiation result in strong heating of the emission time. electron gas and in the generation of nonequilibrium LO phonons, which slow down the processes of electron cooling. Estimates yield a value of about 5000 K 2. PHOTOLUMINESCENCE for the electron temperature just after the termination of IN QUANTUM WELLS FOR HIGH-INTENSITY a pump pulse. Thus, the electrons are distributed PICOSECOND EXCITATION between the upper subbands. Due to the electron gas We studied three-period structures with stepped cooling, the electron concentration decreases in sub- QWs. The width of the narrow band e3 and increases in subband e2, thereby increas- In0.2Ga0.8As/Al0.2Ga0.8As QW is 6 nm, the width of the

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

120 VOROB’EV et al.

Sample F173 Pumping wide Al0.2Ga0.8As/Al0.28Ga0.72As QW is 21.2 nm, and 4 T = 77 K intensity the layers with QWs are separated by Al0.28Ga0.72As 2 Pumping power 0.28 W 3 35 W/cm barriers 20 nm wide. The layers are placed at the center 2 1038 of a waveguide formed by AlGaAs layers with variable L 10–2 70 composition and built into the i layer of the pÐiÐn struc- α 1 1097 102 ture. The samples were optically excited by the second 90 PL intensity, arb. units 0 185 1000 1100 1200 harmonic of the pulsed Nd : YLF laser (λ = 523.5 nm, 145 Energy, meV pulse energy is 4.5 µJ, ∆t = 3.2 ps). Due to the high level of PL excitation by picosecond Absorption 10–3 laser pulses, an appreciable population of upper size- quantization subbands is achieved. Observation of interband electronic transitions from the upper levels is 0 also simplified due to superluminescence. 50 100150 200 250 The results of the study of surface PL are shown in Energy, meV Fig. 2. Under certain conditions, the PL spectrum exhibited clearly defined peaks, which may be related Fig. 3. Photoinduced absorption spectra for undoped QDs. to superluminescence. This phenomenon can be PL spectrum is shown in the inset. observed for high excitation levels because of the amplification of stimulated radiation in the waveguide, even in the absence of a resonator [2]. For radiation to be amplified, a sufficiently large free path of the light (a) wave is needed. Therefore, when the excitation region is small, the superluminescence disappears and only Absorption wide bands of spontaneous PL are observed. There is 0.15 Sample F191 satisfactory agreement between the spectral positions T = 77 K of PL lines and the calculated energies of interband 0.10 Emission Emission transitions in QWs and barriers. For high excitation levels, the number of nonequi- 0.05 librium LO phonons becomes very large during energy relaxation of hot electrons and the electron energy relaxation rate drops by one or two orders of magni- 0 tude. On the other hand, under these conditions, the Absorption, arb. units lifetime of nonequilibrium electronÐhole pairs (of the –0.05 order of 100 ps) is small compared to the interband recombination time. The electron energy relaxation 100 140 180 220 240 time and the electron lifetime become similar; for this Energy, meV reason, the amplitudes of the peaks related to upper excited states become comparable to the amplitude of (b) the fundamental peak. The dependence of the inte- 0.12 Sample F191 grated PL intensity on the pump intensity I is sublinear T = 77 K for I > 109 W/cm2; in this case, the Auger processes 0.10 begin to play an important role in interband recombination. 0.08 The PL intensity measured from the end face of the 0.06 structure in the direction of propagation of the waveguide mode is two orders of magnitude higher. 0.04 hν = 120 meV This allows one to study superluminescence in more 0.02 detail. For unpolarized light, the measured PL spectra Peak amplitude, arb. units are shown in Fig. 3. At sufficiently high pumping lev- 0 els, bright superluminescence lines are observed simul- 0.2 0.4 0.6 0.8 1.0 1.2 1.4 taneously for all spectral intervals corresponding to Pumping power, W interband transitions.

3. INTRABAND ABSORPTION AND EMISSION Fig. 4. (a) Absorption spectrum for background radiation OF LIGHT IN QUANTUM DOTS related to electron transitions between QD levels in undoped QDs and (b) peak absorption as a function of the Both doped and undoped structures with 15 InAs pumping power. QD layers covered by In0.12Ga0.88As layers in the GaAs

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 INTRABAND ABSORPTION AND EMISSION OF LIGHT 121 matrix were studied. The surface density of dots in one When investigating intraband light absorption in layer was 3 × 1010 cmÐ2. Since we plan to use the doped samples in the absence of interband illumina- undoped structure for further studies under the condition, the p-polarized light absorption due to electrons tions of generation of stimulated interband radiation, and the s- and p-polarized light absorption due to holes the QDs in this structure were placed in a waveguide were observed. The absorption intensities for electrons formed by AlGaAs layers of variable composition. and holes are similar. This result poorly agrees with Samples intended for measurements of absorption were theoretical calculations predicting a smaller probability fabricated in multipass geometry. Nonequilibrium car- for hole transitions. Note that there is no contribution riers were generated under interband optical pumping from holes to the photoinduced absorption spectra. This by Ar laser radiation. can be due to the concentrations of photoexcited holes in undoped samples being low. Figure 3 shows the spectrum of photoinduced intraband light absorption for an undoped sample. The features of the spectrum are in good agreement with the ACKNOWLEDGMENTS calculated energy positions of intraband optical transi- The study was supported by INTAS, the Russian tions between QD levels and the values of the corre- Foundation for Basic Research, the Ministry of Indus- sponding matrix elements. try, Science, and Technology of the Russian Federation, For interband illumination, the background radia- and the Ministry of Education of the Russian Federa- tion in the mid-IR range passing through the sample is tion. modulated due to variations in the absorption and reﬂection coefﬁcients, which are affected both by non- REFERENCES equilibrium free carriers and by carriers trapped in 1. A. Kastalsky, L. E. Vorobjev, D. A. Firsov, et al., IEEE J. QDs. Subtracting the contribution of free electrons Quantum Electron. 37 (10), 1356 (2001). from the obtained spectra, we can determine the contribution from electron transitions between QD levels to 2. V. Ya. Aleshkin, S. A. Akhlestina, B. N. Zvonkov, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 29 (4), 590 photoinduced absorption (Fig. 4a). In Fig. 4a, the neg- (1995) [Semiconductors 29, 307 (1995)]. ative peaks may be related to spontaneous transitions between QD levels and the positive peaks, to absorption, which saturates for high pumping levels (Fig. 4b). Translated by I. Zvyagin

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 122Ð124. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 123Ð125. Original Russian Text Copyright © 2004 by Kristovskiœ, Kozhanov, Dolzhenko, Ivanchik, Watson, Khokhlov. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Photoconductivity of Lead Telluride-Based Doped Alloys in the Submillimeter Wavelength Range K. G. Kristovskiœ*, A. E. Kozhanov*, D. E. Dolzhenko*, I. I. Ivanchik*, D. Watson**, and D. R. Khokhlov* *Faculty of Physics, Moscow State University, Vorob’evy gory, Moscow, 119899 Russia e-mail: [email protected] **Department of Physics and Astronomy, University of Rochester, New York, USA

Abstract—Persistent photoconductivity in a Pb0.75Sn0.25Te(In) alloy initiated by monochromatic submillimeter-range radiation at wavelengths of 176 and 241 µm was observed at helium temperatures. This photoconductivity is shown to be associated with optical excitation of metastable impurity states. © 2004 MAIK “Nauka/Interperiodica”.

Most of the presently used high-sensitivity nonther- making standard spectral measurements impossible. An mal detectors intended for use in the far infrared range instrument that has no background illumination at all are based on doped silicon and germanium. The longest but provides the possibility of illuminating a sample wavelength corresponding to the photoelectric thresh- with radiation of a fixed wavelength and calibrated old in such radiation detectors that has been reached in intensity is required. uniaxially strained Ge : Ga was λ = 220 µm [1]. r Such an instrument was built and described in [4] A viable alternative to the silicon- and germanium- (Fig. 1). A sample was fixed to the bottom of a helium based radiation detectors is offered by lead tellurideÐ bath in evacuated space. The background radiation was based narrow-gap semiconductors. Doping lead tellu- eliminated by means of screens cooled to liquid-helium ride and its solid solutions by Group III elements gives and liquid-nitrogen temperatures. Blackbody radiation rise to effects not characteristic of the starting material, with a temperature of 77 or 300 K impinged on the such as Fermi level stabilization and persistent photoconductivity [2]. In particular, the Fermi level in Pb1 − xSnxTe(In) alloys with a tin content of 0.22 < x < 0.28 stabilizes within the band gap to produce semi- insulating states of the semiconductor at low temperatures. Because the effect of Fermi level stabilization brings about homogenization of the electrophysical 8 parameters of the material and because the characteris- 7 tic energy parameters of the alloy, such as the band gap 6 width and the impurity-state activation energy, are of 5 the order of a few tens of millielectronvolts, the possi- T = 4.2 K bility of employing these semiconductors as radiation 4 detectors in the far IR range appears extremely attractive. This possibility was realized [3], and it was found T = 77 K that the sensitivity parameters of a Pb0.75Sn0.25Te(In)- 3 based IR radiometer substantially exceed those of their counterparts based on doped silicon and germanium. T = 300 K However, the key question of the spectral response 2 of the Pb1 Ð xSnxTe(In)-based radiation detector, in particular, of the red cutoff of the photoeffect in this mate- 1 rial, has remained unexplored. The phenomenon of per- Fig. 1. Setup for measuring photoconductivity spectra of sistent photoconductivity observed in Pb1 Ð xSnxTe(In) Pb1 Ð xSnxTe(In) [4]: (1) blackbody, (2) entrance window, at low temperatures results in a buildup of nonequilib- (3) “nitrogen” filter, (4) “helium” filter, (5) interference fil- rium carriers in the allowed band under background ter, (6) rotating disk with filters, (7) sample, and (8) helium radiation present in each standard spectrometer, thus bath.

PHOTOCONDUCTIVITY OF LEAD TELLURIDE-BASED DOPED ALLOYS 123 sample through the entrance window and a series of cooled ﬁlters. Special ﬁlters, which were maintained at 6 the liquid-nitrogen or liquid-helium temperature, trans- 176 µm

mitted only the part of the radiation corresponding to A µ the spectral interval under study. The diaphragm in the µ 241 m “helium” screen made it possible to calibrate the radia- –2 4 tion flux striking the sample. Finally, a narrow radiation line was isolated by means of an interference filter mounted on a rotating disk within the helium screen. 2 Current, 10 However, the interpretation of the results mentioned above has remained open to question. Indeed, the thermal activation energy Ea was calculated from an analysis of the temperature dependence of the resistivity by 0 200 400 600 800 ρ ρ using the relation ~ exp(Ea/2kT) rather than ~ Time, s exp(Ea/kT), as is usually accepted when of dealing with impurity states. The calculations made by using the first Fig. 2. Kinetics of the rise and fall of the photocurrent plot- of the above relations were based on a study of the char- ted for a voltage of 10 mV across the sample and different pump wavelengths. The arrows indicate the times the IR acter of the pressure-induced motion of the impurity illumination is turned on and off. level [5]. However, this substantiation is of an indirect nature. If the activation energy of an impurity level is calculated using the second relation, the value of Ea will plots the experimental data obtained for a sample volt- be one-half of that obtained from the first relation; i.e., age of 10 mV and a blackbody temperature of 300 K. it will correspond to a wavelength of 140 µm. There- fore, the conclusion that the metastable impurity states A noticeable photoresponse was detected at both provide a major contribution to the photoresponse at wavelengths of the radiation striking the sample. wavelengths of 90 and 116 µm will be invalid. Because our sensitive measuring equipment made it possible to record currents of up to 0.25 µA, we could In this paper, we report on the detection of a photo- reliably measure the kinetics of the increase in the pho- response in a Pb0.75Sn0.25Te(In) film at wavelengths of tocurrent only at low voltages across the sample, U < 176 and 241 µm. Pb Sn Te(In) films were grown 40 mV. At higher voltages, the photocurrent grew so 0.75 0.25 fast that the amplifier became overloaded in a time through molecular-beam epitaxy on a BaF2 substrate. The thermal activation energy of the impurity ground comparable to the time required to rotate the filter disk, state calculated from the relation ρ ~ exp(E /2kT) was i.e., within a few seconds. The following features in the a photoconductivity may be of interest here. First of all, 20 meV. The experiment was carried out in the setup the current rise observed after switching on the illumi- shown schematically in Fig. 1. The temperature of the nation follows a strongly nonlinear kinetics. Switching helium screen after filling the helium bath with a cool- off the illumination triggers a fast decay of the photo- ing agent reached a stationary level in ~30 min. The current, with subsequent slow relaxation to the dark disk with the filters was initially set in the position level. If, however, the illumination is switched on again where the blackbody radiation impinged on the metal a short time after its removal, the photocurrent rises shutter. Since it was fixed to the bottom of the helium very fast (in a time comparable to the “fast” relaxation bath, the sample was cooled faster than the screen and time) to the value recorded just before the illumination the disk. Therefore, the sample was initially illuminated removal, after which the previous, relatively slow by the background radiation of the screen and the disk dynamics of the increase in the photocurrent sets in that had not yet cooled down. This background illumi- again. The fast and the slow processes are apparently of nation gave rise to the generation of long-lived non- essentially different natures. equilibrium carriers in the sample. To transfer the sample to the unperturbed state, it was warmed with a Another feature may also be noteworthy. The ener- heater, located close to the sample, after the screen gies of photons corresponding to radiation wavelengths cooling. The increase in the sample temperature to of 176 and 241 µm are substantially less than the ther- 30 K and subsequent cooling to liquid-helium temper- mal activation energy of the impurity ground state, even ature transferred the electronic system of the sample to if this energy is calculated using the relation ρ ~ a close-to-ground state, with practically all the carriers exp(Ea/kT). Thus, the results obtained in this study pro- localized. After this, the disk was rotated such that the vide direct evidence for the persistent photoconductiv- radiation with the wavelength determined by the disk ity in Pb1 Ð xSnxTe(In) originating from photoexcitation filter was directed onto the sample. This rotation usu- of metastable impurity states. The threshold energy for ally lasted 3 to 4 s. We studied the kinetics of the current optical excitation of these states is very low. The wave- increase through the sample for various voltages across length of the corresponding photon is longer than at the sample and various blackbody temperatures. Figure 2 least 241 µm, which, as far as we know, is the largest

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

124 KRISTOVSKIŒ et al. λ value of r for nonthermal radiation detectors. The pho- REFERENCES toconductivity cutoff of the materials studied here 1. E. E. Haller, M. R. Hueschen, and P. L. Richards, Appl. apparently lies at substantially longer wavelengths. Phys. Lett. 34, 495 (1979). One cannot rule out the possibility that the operating 2. B. A. Volkov, L. I. Ryabova, and D. R. Khokhlov, Usp. range of Pb1 Ð xSnxTe(In)-based photodetectors extends Fiz. Nauk 172, 875 (2002) [Phys. Usp. 45, 819 (2002)]. over the whole submillimeter range. 3. S. N. Chesnokov, D. E. Dolzhenko, I. I. Ivanchik, and D. R. Khokhlov, Infrared Phys. 35, 23 (1994). 4. D. R. Khokhlov, I. I. Ivanchik, S. N. Raines, et al., Appl. ACKNOWLEDGMENTS Phys. Lett. 76, 2835 (2000). 5. B. A. Akimov, V. P. Zlomanov, L. I. Ryabova, et al., Fiz. This study was supported in part by the Russian Tekh. Poluprovodn. (Leningrad) 13, 1293 (1979) [Sov. Foundation for Basic Research (project nos. 01-02- Phys. Semicond. 13, 759 (1979)]. 16356, 02-02-17057, 02-02-08083), INTAS (project no. 2001-0184), and a NATO Collaborative Linkage Grant. Translated by G. Skrebtsov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 125Ð129. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 126Ð130. Original Russian Text Copyright © 2004 by Aleshkin, Veksler, Gavrilenko, Erofeeva, Ikonnikov, Kozlov, Kuznetsov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Shallow-Impurity-Assisted Transitions in the Course of Submillimeter Magnetoabsorption of Strained Ge/GeSi(111) Quantum-Well Heterostructures V. Ya. Aleshkin*, D. B. Veksler*, V. I. Gavrilenko*, I. V. Erofeeva*, A. V. Ikonnikov*, D. V. Kozlov*, and O. A. Kuznetsov** * Institute of Microstructure Physics, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected] ** Physicotechnical Research Institute, Nizhni Novgorod State University, pr. Gagarina 23/5, Nizhni Novgorod, 603950 Russia

Abstract—The submillimeter ( f = 130Ð1250 GHz) magnetoabsorption spectra of strained Ge/GeSi(111) multilayer heterostructures with quantum wells are investigated at T = 4.2 K upon band-gap optical excitation. It is found that the magnetoabsorption spectra contain lines associated with the excitation of residual shallow acceptors. The resonance absorption observed can be initiated by optical transitions between the impurity states belonging to two pairs of Landau levels of holes in germanium quantum-well layers. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION magnetic fields, the resistance of samples increases significantly, which results in a substantial decrease in the Shallow-level impurities in quantum-well hetero- signal-to-noise ratio. structures have often been studied using far-IR impurity photoconductivity spectroscopy. In recent years, The purpose of this work was to investigate the mag- this method has been successfully applied to acceptors netoabsorption in Ge/GeSi quantum-well heterostruc- in strained Ge/GeSi heterostructures with quantum tures with residual shallow acceptors upon band-gap wells [1Ð7]. It has been demonstrated that the valence optical excitation. It was shown that this method is an band splitting caused by both elastic strains of layers efficient tool for investigating shallow-impurity- and quantum-confinement effects leads to a substantial assisted optical transitions in quantum wells. decrease in the effective mass of holes in the quantum- well plane and, as a consequence, to a lower binding 2. SAMPLES AND EXPERIMENTAL TECHNIQUE energy of acceptors as compared to those characteristic of bulk germanium. In our earlier works [1, 5, 7], The Ge/Ge1 Ð xSix heterostructures were grown important information on the energy spectrum of impu- through vapor-phase epitaxy on lightly doped Ge(111) rity centers was obtained by measuring the photocon- substrates. The total thickness of all the structures ductivity spectra in strong magnetic fields. It was grown exceeded the critical value, which led to relax- revealed that these spectra contain lines associated with ation of elastic stresses at the heterostructureÐsubstrate the transitions 1s 2p+ and 1s 2pÐ for acceptors interface. As a result, the GeSi layers in the heterostruc- located at the centers of germanium quantum wells and ture turned out to be biaxially extended, whereas the Ge at the centers of GeSi barrier layers. However, in strong layers were biaxially compressed. The materials were

Table 1. Parameters of the Ge/Ge1 Ð xSix heterostructures ε Sample no. xdGe, Å dGeSi, Å Number of periods Strain in Ge layers xx Substrate 262b 0.14 120 300 216 3.8 × 10Ð3 GÉS-45 307a 0.09 300 230 162 8.7 × 10Ð4 GÉS-45 308a 0.09 350 160 162 4.4 × 10Ð4 GÉS-45 308b 0.09 330 150 162 4.4 × 10Ð4 GDG-40 309a 0.07 850 200 83 4.6 × 10Ð4 GÉS-45 309b 0.07 800 200 83 3.3 × 10Ð4 GDG-40

126 ALESHKIN et al.

CH1 not specially doped, and the concentration of residual acceptor impurities in the samples was of the order of CI3 CI1 CE 14 Ð3 CI2 1L 10 cm [1]. The parameters of the studied samples of the Ge/Ge1 Ð xSix heterostructures are presented in Table 1. CH1 The samples were placed in a light-pipe helium cryostat at the center of a superconducting solenoid. Backward- CI3 CI CI1 6 0 2 CE1L wave tubes (BWT) were used as submillimeter radia- CH1 tion sources. The magnetoabsorption spectra were CE 5 recorded at a constant frequency of BWT radiation and CI CI1 1L 0 CI3 2 magnetic-field sweeping in the Faraday configuration Eω ⊥ H at T = 4.2 K. The magnetic field was directed CH1 along the heterostructure axis. The experiments were CI1 CI2 performed with both linearly and elliptically polarized 0 CE1L 4 Ch1 microwave radiation. The elliptic polarization was used CH1 3 to determine the sign of charge carriers and was

Absorption, arb. units achieved with a reflection-type grid polarizer, which CI1 CE1L CI2 ensured a controlled phase shift between two plane 0 Ch1 waves linearly polarized in mutually perpendicular CH1 2 directions. The sample was subjected to band-gap opti- CI1 cal excitation (modulated with a frequency of 1 kHz) 0 with the use of a gallium arsenide light-emitting diode CE1L λ ≈ µ Ch1 ( 0.9 m) located near the sample in liquid helium. The radiation passed through the sample was detected 1 using an n-InSb crystal according to a standard scheme 0 5 10 15 20 25 of lock-in amplification. The signal from the output of H, kOe the amplifier was entered on a personal computer as a function of the magnetic field with the use of an analog- Fig. 1. Magnetoabsorption spectra of sample 308b. បω = to-digital converter. The possibility of observing the (1) 1.39, (2) 1.67, (3) 1.96, (4) 2.40, (5) 2.65, and (6) 2.95 meV. lines of impurity-assisted transitions in magnetoabsorption spectra upon band-gap photoexcitation stems from the fact that generated free electrons and holes can be captured both by ionized impurities (always contained in the samples due to impurity compensation) 5 CH1 and by neutral impurities, which leads to modulation of the impurity absorption. Moreover, strip ohmic con- CE1L tacts were deposited on the sample surface, which made 4 it possible to apply a lateral electric field to the sample. CI3 CI2 CI1 For a number of samples, we measured the submillime- 3 ter photoconductivity spectra. In this case, a bias voltage of approximately 1 V was applied to the sample and , meV Ch1 the submillimeter radiation was modulated with a fre- ω

ប 2 quency of 200 Hz [5]. 1 Ci1 2 1 3. RESULTS AND DISCUSSION Figure 1 shows typical magnetoabsorption spectra 0 5 15 25 35 of sample 308b. Figure 2 presents the calculated and H, kOe experimental data on the energy positions of the resonance lines in the magnetoabsorption spectra and the results of measurements of the photoconductivity spec- Fig. 2. Energy positions of the resonance lines in (1) the tra. By analogy with the results of investigations into magnetoabsorption spectra and (2) photoconductivity spec- the magnetoabsorption upon band-gap photoexcitation បω ӷ tra of sample 308b. Solid lines indicate the calculated ener- of free carriers in quantizing magnetic ﬁelds c kBT gies of the transitions 0s 1s (the CH absorption ω 1 1 1 (where c is the cyclotron frequency of charge carriers) line) and 3a1 4a1 (the Ch1 absorption line) between for other samples of Ge/GeSi heterostructures [8Ð12], it the Landau levels (the computational procedure and the notation of the Landau levels are described in [7Ð10]). The is reasonable to assign the fundamental absorption line dashed line represents the energy positions of the cyclotron CH1 to cyclotron resonance of holes. The case in point resonance line of electrons in the 1L valley (mc = 0.083m0). is the transition from the 0s1 lower lying Landau level

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 SHALLOW-IMPURITY-ASSISTED TRANSITIONS IN THE COURSE 127

4a 1s CH 8 3 3 1s 1 1 1.0 0s3 3a 3 CI1 បω = 1.79 meV 6 4s2 0.8 CI2 4a1 1a2 1 Ch1 0.6 0a2 , meV 4 3s2 ω ប 3a1 0.4 2 0s1 3 2 4 Absorption, arb. units 0.2

0 5 15 25 35 0 4 8 12162024 H, kOe H, kOe

Fig. 3. Calculated energies of the Landau levels of holes in Fig. 4. Magnetoabsorption spectra of sample 308a in a dc the first three quantum-well subbands for sample 308a (the electric field. The intensity of the CI and CI magnetoab- computational procedure is described in [7Ð10]). Designa- 1 2 tions: the first numeral corresponds to the level number; the sorption lines associated with the impurities gradually letters “s” and “a” denote the symmetric and antisymmetric decreases with an increase in the applied electric field, states, respectively; and the subscript indicates the number whereas the CH1 and Ch1 cyclotron lines remains of the quantum-well subband. unchanged. E = (1) 0, (2) 12.5, (3) 22.5, and (4) 35 V/cm.

បω ӷ to the 1s1 level (both levels correspond to heavy holes (2) In quantizing magnetic fields c kBT, the with an angular momentum J = Ð3/2) (Fig. 3). The Ch1 cyclotron resonance spectra can involve not only the line can be associated with the 3a1 4a1 transition CH1 and Ch1 cyclotron lines associated with the transi- between the two lower levels belonging to another lad- tions from two lower Landau levels of holes but also the der of the Landau levels of heavy holes with an angular lines of the intersubband cyclotron transitions (0s1 momentum J = +3/2. It can be seen from Fig. 2 that the 1s3, 0s1 1s5) observed for sample 309 with wide Ge experimental energy positions of these lines are in good quantum wells (dGe = 800–850 Å) [11, 12]. Among the agreement with the results of calculations. The CE1L samples studied in the present work, sample 308 is line is attributed to the cyclotron resonance of elec- characterized by the widest Ge quantum wells (d = 1 Ge trons in the 1L valley, which forms the conduction 330–350 Å). However, even for these quantum wells, band bottom in GeSi layers, i.e., quantum wells for the energy separation between the first and third inter- electrons in the studied structures with thick Ge layers acting quantum-well subbands is equal to 4.4 meV (samples 307Ð309) [11, 12]. In these samples (unlike (Fig. 3), whereas the CI1ÐCI3 impurity lines are clearly the previously studied samples 259 [13], 306 [8Ð10], observed at considerably lower photon energies and 262, in which the conduction band bottom is (Figs. 1, 2). Therefore, the aforementioned lines cannot formed by states of the 3L valleys in Ge layers [14]), the be attributed to the intersubband cyclotron resonance. mean silicon content x and, hence, the elastic strain ε xx (3) The extrapolation of the energy positions of the in the Ge layers are small in magnitude (Table 1). CI1ÐCI3 lines gives a finite (nonzero) energy at H 0 In our opinion, the remaining lines, CI1ÐCI3 and Ci1, (see also [8Ð10]). can be assigned not to cyclotron resonance of free (4) In a dc electric field (with a voltage up to charge carriers but to shallow-impurity-assisted transi- 35 V/cm), the CH and Ch lines associated with the tions. This inference was made for the following rea- 1 1 sons. cyclotron resonance are retained in the magnetoabsorption spectrum (Fig. 4), whereas the intensity of the (1) In magnetic fields whose strength exceeds impurity lines gradually decreases, most likely, as a 10 kOe, the energy separation between the lower Lan- result of impact ionization of impurities. dau levels (0s , 3a ) and the higher lying Landau levels 1 4 (5) As can be seen from Fig. 2, the slope of the exceeds 1 meV (Fig. 3), which is substantially greater curves corresponding to the energy positions of the than kBT (0.36 meV at 4.2 K). Consequently, the popu- CI1ÐCI3 lines is identical to that of the CH1 line. More- lation of higher lying Landau levels is small and the over, the curve describing the energy position of the Ci transitions from these levels should not manifest them- 1 line is parallel to that of the Ch line. A similar behavior selves in the magnetoabsorption spectra. 1 of the impurity lines was observed for samples 309 with 1 This can also be judged from the results of polarization measure- very wide quantum wells (dGe = 850 Å) [11, 12] and for ments similar to those described in [11, 12]. samples with narrower quantum wells, namely, 307a

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 128 ALESHKIN et al.

CI1 assigned to the transitions between the impurity states associated with the 0s1 and 1s1 Landau levels, whereas CI2 the Ci1 line corresponds to the transitions between the CI3 CH CE1L states associated with the 3a and 4a levels. 1 6 1 1 0 CI1 Upon band-gap photoexcitation at a low temperature, generated free electrons and holes can be captured CI2 CE1L both by ionized impurities, i.e., acceptors and donors CI3 CH1 Ch1 (always contained in the sample due to impurity compensation), and by neutral impurities (in our case, CI 5 0 1 acceptors). It is unlikely that the observed resonances CI 2 Ch can be due to transitions involving donor impurities, 1 because, ﬁrst, the structures under investigation possess CI3 CH1 CI1 p-type conductivity (i.e., donors are compensating 4 impurities) and, second, the polarization measurements 0 did not reveal resonance lines with electron polariza-

Absorption, arb. units CH1 Ch1 tion among the impurity lines. Undoubtedly, the com- CI2 CI1 plete interpretation of the impurity lines observed calls 0 3 for further experimental and theoretical investigations. However, we can list all the possible acceptor-assisted CH1 optical transitions. First, this is the 1s 2p+ transi- CI Ch 0 2 1 2 tion for acceptors located in the vicinity of the barrier Ch1 centers. The binding energy reaches a maximum and a minimum at the centers of the quantum well and the CI1 CI2 CH 1 barrier, respectively (Table 2). Therefore, in the case of 1 residual impurities (uniformly distributed throughout 0 5 10 15 20 25 the structure), it is reasonable to expect that the transi- H, kOe tions with energies corresponding to exactly these posi- Fig. 5. Magnetoabsorption spectra of sample 307a. បω = tions of the impurities will manifest themselves in the (1) 1.21, (2) 1.48, (3) 1.70, (4) 1.87, (5) 2.22, and spectra (see, for example, [3, 4]). The binding energies (6) 2.83 meV. typical of acceptors located at the centers of the quantum wells and barriers in Ge/GeSi heterostructures are equal to 7Ð8 and 2 meV, respectively (Table 2). Hence, (dGe = 300 Å) (Figs. 5, 6), 306a (dGe = 200 Å) [8–10], it follows that the energies of the transitions involving and 262b (dGe = 120 Å) (Fig. 7). On this basis, it is rea- acceptors located in quantum wells fall outside the sonable to assume that the CI1ÐCI3 lines can be energy range covered. Second, the magnetoabsorption

5 CH 1 5 1 2 CE1L CH1 4 4 CI2 CI1 CI 3 CI3 2 3 , meV , meV ω ω ប

ប 2 2 Ch1

1 1 CI1

0 5 15 25 35 02 6 10 14 18 22 26 30 H, kOe H, kOe Fig. 6. Energy positions of the resonance lines in the magnetoabsorption spectra of sample 307a (circles): (1) ener- Fig. 7. Energy positions of the resonance lines in the mag- gies of the 0s1 1s1 transition (the CH1 absorption line) netoabsorption spectra of sample 262b (circles). The solid calculated according to the procedure described in [7Ð10] line represents the energies of the 0s1 1s1 transition and (2) the cyclotron resonance line of electrons in the 1L (the CH1 absorption line) calculated according to the proce- valley. dure described in [7Ð10].

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 SHALLOW-IMPURITY-ASSISTED TRANSITIONS IN THE COURSE 129

Table 2. Binding energies of shallow acceptor levels in the REFERENCES Ge/Ge Si heterostructures (meV) 1 Ð x x 1. V. I. Gavrilenko, I. V. Erofeeva, A. L. Korotkov, et al., Sample no. 1s 2p 2s 2p± Pis’ma Zh. Éksp. Teor. Fiz. 65 (2), 194 (1997) [JETP 0 Lett. 65, 209 (1997)]. 262b (well center) 7.9 Resonant 1.3 1.4 2. V. Ya. Aleshkin, V. I. Gavrilenko, I. V. Erofeeva, et al., 262b (barrier center) 2.1 Resonant 0.6 0.93 Fiz. Tekh. Poluprovodn. (St. Petersburg) 32 (10), 1240 (1998) [Semiconductors 32, 1106 (1998)]. 307a (well center) 6.9 2.8 1.2 1.5 3. V. Ya. Aleshkin, V. I. Gavrilenko, I. V. Erofeeva, et al., 307a (barrier center) 1.8 0.6 0.4 0.9 Phys. Status Solidi B 210 (2), 649 (1998). 308a (well center) 7.5 3.1 1.7 2.0 4. V. Ya. Aleshkin, B. A. Andreev, V. I. Gavrilenko, et al., 308a (barrier center) 2.0 0.8 0.5 0.88 Fiz. Tekh. Poluprovodn. (St. Petersburg) 34 (5), 582 (2000) [Semiconductors 34, 563 (2000)]. 309b (well center) 8.4 3.1 2.5 1.8 5. V. Ya. Aleshkin, B. A. Andreev, V. I. Gavrilenko, et al., 309b (barrier center) 1.9 0.9 0.4 Ð Physica E (Amsterdam) 7 (3Ð4), 608 (2000). 6. V. Ya. Aleshkin, B. A. Andreev, V. I. Gavrilenko, et al., Nanotechnology 11 (4), 348 (2000). spectra obtained in this work can exhibit transitions 7. V. Ya. Aleshkin, V. I. Gavrilenko, D. B. Veksler, and between excited acceptors states belonging to different L. Reggiani, Phys. Rev. B 66, 155336 (2002). Landau levels. These transitions can occur under band- 8. V. Ya. Aleshkin, V. I. Gavrilenko, I. V. Erofeeva, et al., in gap photoexcitation, provided the lifetime of charge Proceedings of the Workshop on Nanophotonics (IFM carriers is comparable to the relaxation time scale for Ross. Akad. Nauk, Nizhni Novgorod, 1999), p. 114. hot carriers in the excited states [15]. Finally, the band- 9. V. Ya. Aleshkin, V. I. Gavrilenko, I. V. Erofeeva, et al., in gap photoexcitation can lead to the formation of A+ cen- Proceedings of the 6th International Symposium “Nano- ters due to the capture of an excess hole by a neutral structures: Physics and Technology,” St. Petersburg, acceptor. According to our estimates [16], the binding Russia (1999), p. 356. energy of A+ centers in a quantum well is approximately 10. V. Ya. Aleshkin, V. L. Vaks, D. B. Veksler, et al., Izv. equal to 2 meV; therefore, these centers, as well as the Akad. Nauk, Ser. Fiz. 64 (2), 308 (2000). acceptors located in the barriers, can manifest them- 11. V. Ya. Aleshkin, D. B. Veksler, V. I. Gavrilenko, et al., in selves in the spectra. Proceedings of the Workshop on Nanophotonics (IFM Ross. Akad. Nauk, Nizhni Novgorod, 2003), p. 11. 12. V. Ya. Aleshkin, D. B. Veksler, V. I. Gavrilenko, et al., Fiz. Tverd. Tela (St. Petersburg) 46 (1), 131 (2004) ACKNOWLEDGMENTS [Phys. Solid State 46, 130 (2004)]. We would like to thank M.D. Moldavskaya for long- 13. V. I. Gavrilenko, I. N. Kozlov, O. A. Kuznetsov, et al., Pis’ma Zh. Éksp. Teor. Fiz. 59 (5), 327 (1994) [JETP term cooperation laying the groundwork for the present Lett. 59, 348 (1994)]. study, E.A. Uskova for preparing the samples use in our 14. V. Ya. Aleshkin and N. A. Bekin, Fiz. Tekh. Polupro- measurements, V.L. Vaks and A.N. Panin for their assis- vodn. (St. Petersburg) 31, 171 (1997) [Semiconductors tance in performing the experiments with backward- 31, 132 (1997)]. wave tubes, and Yu.N. Drozdov for x-ray diffraction 15. S. V. Meshkov and É. I. Rashba, Zh. Éksp. Teor. Fiz. 76 investigations of the samples. (6), 2206 (1979) [Sov. Phys. JETP 49, 1115 (1979)]. This work was supported by the Russian Foundation 16. V. Ya. Aleshkin, V. I. Gavrilenko, and D. V. Kozlov, in Proceedings of the Workshop on Nanophotonics (IFM for Basic Research (project no. 03-02-16808); the Min- Ross. Akad. Nauk, Nizhni Novgorod, 2003), p. 318. istry of Industry, Science, and Technology of the Rus- sian Federation; and the Russian Federal program “Integration” (project no. B0039/2102). Translated by O. Borovik-Romanova

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 13Ð16. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 18Ð20. Original Russian Text Copyright © 2004 by Bresler, Gusev, Terukov, Froitzheim, Fuhs.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Edge Electroluminescence of Silicon: An Amorphous-SiliconÐCrystalline-Silicon Heterostructure M. S. Bresler*, O. B. Gusev*, E. I. Terukov*, A. Froitzheim**, and W. Fuhs** *Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia **Hahn-Meitner-Institut, Abt. Silizium-Photovoltaik, Kekule-Str. 5, Berlin, D-12489 Germany

Abstract—Silicon edge electroluminescence (EL) was observed on an amorphous-siliconÐcrystalline-silicon heterostructure (a-Si : H(n)/c-Si(p)) in the temperature range from 77 to 300 K. The room-temperature EL internal quantum efﬁciency of the heterostructure under study was found to be about 0.1%. A theoretical analysis of the emissive properties of the a-Si : H(n)/c-Si(p) heterostructure was made in terms of the model of an abrupt planar pÐn junction and showed that, for optimal doping, the internal quantum efﬁciency of the EL may be as high as a few percent at a modulation frequency of about 50 kHz. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION prepared through deposition of hydrogenated amor- The demand for high-efficiency photonic materials phous silicon, a-Si : H, on a c-Si(p) (crystalline p-sili- capable of being integrated into standard optical fiber con) substrate. In the course of deposition, the amorphous silicon was doped by phosphorus to a concentra- communications lines stimulated interest in the light- 19 Ð3 emitting properties of silicon. Among the various tion of 10 cm . The a-Si : H(n) film thus obtained was approaches for silicon-based optoelectronics, the most 30 nm thick. An 80-nm-thick transparent conducting straightforward path lies in increasing the efficiency of electrode for coupling the light out of the a-Si : H(n) the intrinsic edge electroluminescence (EL) of silicon. layer was applied by sputtering ZnO(Al). A ring con- An internal quantum efficiency of the EL of about 1% tact was produced on the ZnO(Al) surface through the was recently claimed to have been reached in a pÐn deposition of aluminum. crystalline-silicon homojunction [1, 2]. This value, The currentÐvoltage curves of the a-Si : H(p)/c- which is fairly high for silicon, was explained in terms Si(n) electroluminescent heterostructure measured at of the EL model based on an abrupt planar silicon pÐn 77 and 300 K are displayed in Fig. 1. Electrolumines- junction [3]. cence was observed by passing square current pulses In this communication, we show that the amorphous through the forward-biased structure and was analyzed n-siliconÐcrystalline p-silicon electroluminescent het- by a grating monochromator with a focal length of erostructure, a-Si : H(n)/c-Si(p), operates similar to a pÐn homojunction based on crystalline silicon; namely, the passing of a current through a forward-biased a- 20 Si : H(n)/c-Si(p) heterostructure generates silicon edge EL due to exciton recombination in crystalline silicon. 12 Similar to the case of a pÐn junction based on crystal- 10 line silicon, the internal quantum efficiency of an a- Si : H(n)/c-Si(p) heterostructure is governed by the radiative recombination coefficient and by the lifetime of the electrons injected into the c-Si(p) conduction Current, mA 0 band. The electroluminescent a-Si : H(n)/c-Si(p) heterostructure can have a higher external EL quantum efficiency than a pÐn homojunction based on crystalline 12 silicon. –10 –3 –2 –1 0 1 Voltage, V 2. EXPERIMENTAL RESULTS Fig. 1. IÐV characteristics of an amorphous-silicon-crystal- The amorphous n-siliconÐcrystalline p-silicon elec- line-silicon heterostructure measured at (1) 300 and troluminescent heterostructure a-Si : H(n)/c-Si(p) was (2) 77 K.

14 BRESLER et al.

20 was recorded using a digital oscillograph. The total 4 time resolution of the measuring system was 3 µs. 16 3 1 Figure 2 presents the current dependence of the EL 2 1 intensity of the a-Si : H(n)/c-Si(p) heterostructure taken 2 at temperatures of 77 and 300 K. The inset shows the 12 1 EL spectra obtained at these temperatures. The spectra 0 are due to conventional edge luminescence of crystal- 8 EL intensity, arb. units 1.0 1.1 1.2 1.3 Wavelength, µm line silicon. At low temperature, practically all of the 2 intrinsic silicon EL originates from the recombination 4 of free electrons with the involvement of optical EL intensity, arb. units phonons. At room temperature, the recombination contributions from free excitons and free carriers are 0 5 10 15 20 approximately equal; for this reason, the top of the Current, mA room-temperature spectrum is slightly deformed. As is evident from Fig. 2, the room-temperature EL intensity Fig. 2. Silicon edge EL intensity vs. current density mea- is considerably higher than that measured at liquid- sured at (1) 300 and (2) 77 K at the maximum of the corre- nitrogen temperature. The edge luminescence decay sponding spectral line. Inset shows EL spectra obtained at the same temperatures. time measured after the current pulse was turned off at room temperature was 25 µs against less than 3 µs at liquid-nitrogen temperature. Figure 3 shows the temperature behavior of the integrated intensity of the 0.4 intrinsic EL. We readily see that the intrinsic EL intensity increases with temperature and reaches a maximum at room temperature. Note that similar results on 0.3 the temperature course of the intensity and decay time of the edge EL have been observed in a crystalline-sili- 0.2 con pÐn homojunction [1Ð3].

0.1 3. RESULTS AND DISCUSSION

Integrated intensity, arb. units Figure 4 presents an energy diagram of the a-Si : H(n)/c-Si(p) heterojunction based on data from [4]. The 0 100 150 200 250 300 gap widths of a-Si : H and c-Si are 1.9 and 1.12 eV, T, K respectively. The band offset in the conduction band is approximately 0.2Ð0.3 eV. The Fermi level for the Fig. 3. Temperature dependence of the integrated intensity a-Si : H layer doped by phosphorus to 1019 cmÐ3 lies of silicon edge EL. 0.25 eV below the conduction-band bottom [4]. In this case, the electron concentration in the conduction band corresponding to the given Fermi level position (6 × E c 1016 cmÐ3) is fairly low for the emitter. At the interface pocket, however, the concentration may reach 5 × Vbi c-Si(p) 1018 cmÐ3, a level high enough to attain efﬁcient electron injection.

EF The analysis of the electroluminescence efficiency Ev of a crystalline-silicon pÐn junction carried out in [3] a-Si:H(n) showed that a high doping level in the n region of a homogeneous pÐn junction favors the achievement of a good electroluminescence efficiency. In this case, the edge silicon EL would be governed primarily by the p region and the internal edge EL quantum efficiency can be written as E τ η ≈≈τ ------g ----n Fig. 4. Energy band diagram for a-Si : H/c-Si. rr p p n τ , (1) qVbi τ

where rr is the radiative recombination coefﬁcient, pp is 822 mm equipped with a cooled germanium photode- the concentration of majority carriers (holes) in the p τ tector. The EL decay after the current was turned off region of the pÐn junction, n is the total electron lifetime in the p region, Eg is the band-gap width of c-Si,

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 EDGE ELECTROLUMINESCENCE OF SILICON 15 q is the electronic charge, and Vbi is the potential barrier in the conduction band. Thus, the internal quantum efﬁ- 4 ciency is determined, as follows from Eq. (1), by the ratio of the total minority-carrier to radiative lifetime. 3 Because the lifetimes depend on the concentrations of majority carriers in the n and p regions, these regions can be doped to an optimum level. Using the data on the 2 dependence of the minority-carrier lifetime on the majority-carrier concentration [5], one can readily cal- 1

culate the optimum doping level needed to attain the Quantum efficiency, % maximum possible internal quantum efficiency of intrinsic EL. The results of the calculation are plotted in 0 1016 1017 1018 1019 Fig. 5. We readily see that the maximum quantum effi- –3 ciency of the edge EL may be as high as 3% at a p- Concentration, cm region carrier concentration of 1017 cmÐ3. At higher concentrations, the quantum efficiency degrades Fig. 5. Calculated dependence of the edge EL quantum effi- τ ciency on the doping level of the p region in the pÐn junc- because of the decrease in n brought about by Auger tion. T = 300 K. Carrier concentration in the n region 5 × processes, while at low concentrations the radiative 1018 cmÐ3. recombination probability is low. Ð14 Ð3 Ð1 Using rr ~ 10 cm s for the room-temperature surface states at the amorphous siliconÐcrystalline sili- τ Ð4 radiative recombination coefficient [6] and n ~ 10 s con interface may give rise to the same effect. for the minority carrier lifetime in c-Si(p) for an equi- It is appropriate to compare here the emissive prop- librium charge concentration of 1 × 1016 cmÐ3 [5], we Ð2 erties of a pÐn homojunction based on crystalline sili- estimated the internal quantum efficiency as 10 . This con and of the a-Si : H/c-Si heterostructure. The exter- value of the internal quantum efficiency is noticeably nal quantum efficiency of the a-Si : H/c-Si electrolumi- higher than the experimental value (0.1 × 10Ð2). nescent structure will be somewhat higher, because the We believe that this discrepancy may be due to the edge radiation of silicon is coupled out through the low quality of our pÐn junction. This conjecture is sup- a-Si : H wide-gap material, which reduces the edge EL ported by the temperature dependence of the integrated absorption. Since the technique used to prepare the EL intensity displayed in Fig. 3. Because the radiative a-Si : H(n)/c-Si(p) heterostructures is simpler and considering the compatibility of these structures with the recombination coefficient rr should decrease with increasing temperature [6], the growth of the integrated optical devices employed in silicon-based optoelec- intensity of intrinsic EL with temperature should be tronics, we believe that these structures may find appli- assigned, as in the case of the crystalline-silicon pÐn cation in this area. homojunction, to the fact that the probability of trapping of the electrons injected into the p region by deep 4. CONCLUSIONS impurities (defects) decreases with increasing temperature. Thus, we believe that the n region of our pÐn junc- Thus, we have observed silicon EL in the amor- tion contains a certain concentration of deep attracting phous siliconÐcrystalline silicon heterojunction in the recombination centers. The formation of such centers is region extending from nitrogen temperature to room apparently connected with the penetration of defects temperature. The temporal characteristics of the edge into the n region in the course of deposition of the EL and the temperature behavior of its intensity in amorphous p-silicon layer. such a structure are very close to those observed with The first excited metastable level of a deep charged a homogeneous pÐn junction based on crystalline sili- impurity is known to be close, in order of magnitude, to con. However, the lower energy barrier between the the energy of a shallow acceptor (donor) in silicon; i.e., a-Si : H(n) and c-Si(p) conduction bands and the this level is ~50 meV relative to the edge of the valence larger band-gap width of amorphous silicon may pro- or conduction band. At room temperature, the rate of vide favorable conditions for attaining higher internal electron trapping to the metastable level mediating the and external quantum efficiencies of edge EL in the multiphonon electron capture to the ground state can be a-Si : H(n)/c-Si(p) structure. lower than the rate of reverse carrier ejection from this level into the band. Thus, the probability of nonradia- ACKNOWLEDGMENTS tive trapping of injected electrons by deep centers in silicon decreases with increasing temperature. This is This study was supported by the Russian Founda- what accounts for the increase in the EL intensity and tion for Basic Research, the Netherlands scientific for the observed enhancement of the EL signal decay research foundation (NWO), the Ministry of Industry, time after the termination of the current pulse. Note that Science, and Technology of the Russian Federation,

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 16 BRESLER et al. and the RAS Physical Sciences Division program Ampliﬁcation and Stimulation in Silicon, OASIS, Trento “New Materials and Structures.” (2002). 4. A. Froitzheim, K. Brendel, L. Elstner, et al., J. Non- Cryst. Solids 299Ð302, 663 (2002). REFERENCES 5. V. N. Abakumov, V. I. Perel’, and I. N. Yassievich, Non- 1. M. A. Green, J. Zhao, A. Wang, et al., Nature 412, 805 radiative Recombination in Semiconductors (S.-Peterb. (2001). Inst. Yad. Fiz. Ross. Akad. Nauk, St. Petersburg, 1997). 6. H. Schlangenotto, H. Maeder, and W. Gerlach, Phys. 2. W. L. Ng, M. A. Lourenc, o, R. M. Gwilliam, et al., Status Solidi A 21 (2), 357 (1974). Nature 410, 192 (2001). 3. O. B. Gusev, M. S. Bresler, I. N. Yassievich, and B. P. Zakharchenya, in NATO Workshop on Optical Translated by G. Skrebtsov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 130Ð137. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 131Ð137. Original Russian Text Copyright © 2004 by Aleshkin, Veksler, Gavrilenko, Erofeeva, Ikonnikov, Kozlov, Kuznetsov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Intersubband Cyclotron Resonance of Holes in Strained Ge/GeSi(111) Heterostructures with Germanium Wide Quantum Wells and Cyclotron Resonance of 1L Electrons in GeSi Layers V. Ya. Aleshkin*, D. B. Veksler*, V. I. Gavrilenko*, I. V. Erofeeva*, A. V. Ikonnikov*, D. V. Kozlov*, and O. A. Kuznetsov** * Institute of Microstructure Physics, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected] ** Physicotechnical Research Institute, Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950 Russia

Abstract—The submillimeter (បω = 0.5Ð5 meV) magnetoabsorption spectra of strained Ge/Ge Si (111) ≈ ≈ 1 Ð x x multilayer heterostructures with thick Ge layers (dGe = 300–850 Å, dGeSi 200 Å, x 0.1) are investigated at T = 4.2 K upon band-gap optical excitation. It is revealed that the absorption spectra contain cyclotron resonance lines of 1L electrons localized in GeSi solid solution layers (unlike the previously studied structures with thin Ge layers as quantum wells for 3L electrons). The absorption spectra of the samples with thick Ge layers (dGe = 800–850 Å) exhibit cyclotron resonance lines of holes due to transitions from the lower Landau levels in the ﬁrst quantum-well subband to the Landau levels belonging to the third and ﬁfth higher subbands. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION tron resonance spectra of holes in these heterostructures contain lines attributed to transitions between the Ge/GeSi heterostructures with quantum wells are Landau levels in the first quantum-well subband of car- convenient model objects for studying the transforma- riers. However, cyclotron resonance lines of electrons tion of the energy spectra of charge carriers upon have not been observed. changeover from a bulk semiconductor to strained quantum-well layers. Investigation of these structures In this work, we investigated the magnetoabsorption spectra of Ge/GeSi(111) heterostructures with thick Ge makes it possible to elucidate the combined effects of ≥ elastic strain and quantum confinement (which can be layers (dGe 300 Å) upon band-gap photoexcitation of independently controlled by varying the composition charge carriers. It was revealed that the absorption and thickness of the grown layers) on the energy spec- spectra of all the samples studied exhibit cyclotron res- tra of charge carriers. Up to now, much attention has onance lines of electrons in 1L valleys, which form the been focused on the study of the valence band, in which conduction band bottom in GeSi solid solution layers. it was assumed that the effective mass of charge carriers In heterostructures with the thickest Ge layers (800Ð substantially decreases as a result of the splitting of 850 Å), the energy separation between the quantum- light- and heavy-hole subbands.1 This inference was well subbands of holes and the energies of cyclotron drawn in a number of works concerned with the charge transitions were found to be of the same order of mag- transfer (see, for example, [1]) and cyclotron resonance nitude (up to 5 meV). This made it possible for the first observed in both undoped materials (upon band-gap time to observe the transitions to the Landau levels photoexcitation of carriers) [2] and selectively doped belonging to the highest quantum-well subbands. samples [3]. Earlier [4], cyclotron resonance was examined using samples with relatively thin Ge layers whose ≤ 2. SAMPLES AND EXPERIMENTAL TECHNIQUE thickness (dGe 200 Å) was of the order of the thick- ≈ The Ge/Ge1 Ð xSix heterostructures were grown ness of Ge1 Ð xSix solid solution layers (x 0.1). In these objects, the quantum wells for electrons and holes through vapor-phase epitaxy on lightly doped Ge(111) reside in strained Ge layers and the conduction band substrates. The table presents the structural parameters bottom is formed by states of 3L valleys [4]. The cyclo- and strains for samples 307Ð309 and sample 306a (studied in our previous works), which were deter- 1 In Ge/GeSi heterostructures, quantum wells for holes always mined using x-ray diffraction analysis. The total thick- reside in the Ge layers [4]. ness of all the structures grown exceeded the critical

INTERSUBBAND CYCLOTRON RESONANCE OF HOLES 131

Parameters of the Ge/Ge1 Ð xSix heterostructures ε × 4 Sample no. xdGe, Å dGeSi, Å Number of periods Strain in Ge layers, xx 10 Substrate 306a 0.12 200 260 162 22 GÉS-45 307a 0.09 300 230 162 8.7 GÉS-45 308a 0.09 350 160 162 4.4 GÉS-45 308b 0.09 330 150 162 4.4 GDG-40 309a 0.07 850 200 83 4.6 GÉS-45 309b 0.07 800 200 83 3.3 GDG-40 value, which led to elastic relaxation at the heterostruc- holes, cyclotron resonance of electrons, and different tureÐsubstrate interface. As a result, the Ge layers impurity-assisted transitions. It should be noted that, in turned out to be biaxially compressed in the hetero- our earlier works [2, 6Ð8], we did not observe cyclotron structure, whereas the GeSi layers were biaxially resonance lines of electrons in the magnetoabsorption extended. The materials were not specially doped, and the concentration of residual acceptor impurities was of the order of 1014 cmÐ3 [5]. The samples were placed at CE1L the center of a superconducting solenoid in liquid 18 helium. The magnetic field was directed along the heterostructure axis. Backward-wave tubes were used as CH3 radiation sources in the frequency range f = 130Ð CH5 1250 GHz. The measurements were performed in the Faraday configuration Eω ⊥ H at a constant frequency 7 of microwave radiation and magnetic-field sweeping at 01020 30 40 50 T = 4.2 K. Free charge carriers in the sample were gen- H, kOe erated under band-gap photoexcitation with the use of a gallium arsenide light-emitting diode (λ ≈ 0.9 µm) located near the sample in liquid helium. The radiation CE1L CI CH3 passed through the sample was detected using an n- 4 2 InSb crystal according to a standard scheme of lock-in amplification. The signal from the output of the ampli- 6 fier was entered on a personal computer as a function of CH 3 CE the magnetic field with the use of an analog-to-digital CI2 1L 3 converter. In order to reduce interference effects in the 5 sample, the substrate surface was ground and tapered CH3 ° CE with a wedge angle of 2 . The experiments were carried 1L Ch3 out with linearly and elliptically polarized radiation. Absorption, arb. units CH1 The elliptic polarization was used to determine the sign CE1L 4 CI of charge carriers and was achieved with a reflection- 2 1 CH1 Ch'3 type grid polarizer, which ensured a controlled phase Ch3 shift between two plane waves linearly polarized in CE1L 3 mutually perpendicular directions. Moreover, two strip CI 1 Ch' ohmic contacts (3 to 4 mm apart) were deposited on the CH1 3 Ci1 sample surface, which made it possible to apply a lat- 1 CE1L eral electric field to the sample for heating of charge Ci 2 carriers. 1 CH1 Ci2

3. CYCLOTRON RESONANCE 1 OF 1L ELECTRONS 0510 15 20 25 Figure 1 shows typical cyclotron resonance spectra H, kOe for sample 309a. Figure 2 presents the calculated and experimental data on the energy positions of the reso- Fig. 1. Magnetoabsorption spectra of sample 309a for ellip- nance lines in the magnetoabsorption spectra. These tic polarization of BWT radiation. បω = (1) 0.65, (2) 1.16, (3) 1.34, (4) 1.72, (5) 2.51, (6) 2.81, and (7) 4.73 meV. Solid spectra exhibit a large number of lines, which, most and dashed lines correspond to different directions of the likely, can be attributed to the cyclotron resonance of magnetic ﬁeld.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

132 ALESHKIN et al. ≈ spectra of the Ge/GeSi heterostructures (dGe 200 Å). 5 Figure 3 depicts the calculated (according to the proce- CH5 dure described in [6–9]) “fan-shaped” patterns of the Landau levels of holes in sample 309a for the first five 4 CE1L → quantum-well subbands. By analogy with the results of 0s1 1s5 analyzing the cyclotron resonance spectra of samples 0s →1s CH3 1 3 with narrower quantum wells [6Ð8], it is reasonable to 3 → 0s1 1s1 assume that the fundamental cyclotron resonance line meV in strong magnetic fields is associated with the 0s1 ω, CI2 Ch ប 2 3 1s1 transition from the lower Landau level of holes. It Ch3' can be seen from Fig. 3 that, in the energy range 0.5Ð CI1 Ch1 Ci1 5 meV, the Landau levels of holes in several quantum- 1 Ci2 well subbands interact with each other. In particular, the

CH1 1s1 level (the final state of the basic cyclotron transition 0s1 1s1) anticrosses the 1s3 level in the third quan- 0 5152535 tum-well subband, which, in turn, anticrosses the 1s5 H, kOe level in the fifth subband. This should result in anticrossing of the cyclotron resonance lines in the (H, បω) Fig. 2. Energy positions of the resonance lines in the mag- plane. However, as can be seen from Figs. 1 and 2, the netoabsorption spectra of sample 309a (points). Solid lines indicate the calculated magnetic-field dependences of the principal line CE1L in the spectra is characterized by a energies of the transitions between different Landau levels nearly linear frequency dependence of the resonance of holes in the spectral regions where these transitions occur magnetic field with a slope corresponding to the cyclo- with a sufficiently high intensity. The notation of the Lan- tron mass m ≈ 0.083m . The key to understanding the dau levels is given in the caption to Fig. 3. The calculations c 0 are performed according to the procedure described in [6Ð nature of the CE1L line lies in the results of the polariza- 9] with the following parameters of the hole Hamiltonian tion measurements, which are presented in Fig. 1 (spec- γ γ for Ge quantum wells: A = 0.99 1, B = 1.98 2, and D = tra 7). From analyzing these spectra, it follows that the 1/2γ γ γ γ 2.06(3) 3, where 1, 2, and 3 are the parameters of the observed spectral lines CH5 and CE1L correspond to dif- Luttinger Hamiltonian for holes in bulk Ge [10]. Dashed ferent circular polarizations of radiation. Taken lines represent the energy positions of the cyclotron resonance line of electrons in the 1L valley (m = 0.083m ). together, these facts suggest that the CE1L line can be c 0 attributed to the cyclotron resonance of electrons in the 1L valley forming the conduction band bottom in the GeSi layers (in the strained Ge layers, the 3L valleys of 2 1s 1s 4s 4a electrons are the lowest valleys). The cyclotron reso- 5 3 4a5 1 3 4a1 nance lines of 1L electrons are also observed in the 4s4 4s2 spectra of samples 307a and 308b (Fig. 4). Thus, the experimental results indicate that, in samples 307a, 4 3s 308a, 308b, 309a, and 309b of the Ge/Ge1 Ð xSix hetero- 4 structures with thick Ge layers, the quantum wells for 3a3 3a electrons reside in the GeSi solid solution layers. It can

, meV 1 3s2 ε ω 0s1 be seen from the table that the elastic strain of germa- ប 2 nium layers in these samples is severalfold smaller than that in the previously studied sample 306a. This difference may stem from the fact that the aforementioned samples are characterized by a larger thickness of the Ge layers, a smaller value of x, and, hence, a lower 0 1020304050 mean silicon content in the heterostructure as compared H, kOe to these values for sample 306a. In [4], it was theoretically analyzed how the layer parameters affect the structure of the conduction band bottom in a pseudo- morphically grown layer of Ge/Ge Si . It is seen Fig. 3. Energies of the hole Landau levels in the first five 1 Ð x x quantum-well subbands for sample 309a according to the 2 calculations using the procedure described in [6Ð9] with the The biaxial tension of the GeSi layers in the structure plane is following parameters of the Luttinger Hamiltonian for holes equivalent to a combination of uniform extension (which does not in bulk Ge: A = 13.38 = γ , B = 8.48 = 2γ , and D = 19.34 = affect the crystal symmetry and the structure of the conduction 1 2 band bottom) and uniaxial compression along the [111] axis. As a 1/2γ 2(3) 3 [10]. Designations: the first numeral corresponds result, the 1L valley of electrons shifts toward the low-energy to the level number; the letters “s” and “a” denote the sym- range, whereas the 3L valleys shift toward the high-energy range metric and antisymmetric states, respectively; and the sub- [11]. By contrast, the states of the 3L valleys in biaxially com- script indicates the number of the quantum-well subband. pressed Ge layers are the lower states.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 INTERSUBBAND CYCLOTRON RESONANCE OF HOLES 133 from Fig. 5 that, in the (a||, x) plane, the parameters of CH1 samples 308a, 308b, 309a, and 309b fall in region 3, for which the lowest energy states in the conduction CE1L band correspond to the 1L valley in the Ge1 Ð xSix solid solution. This is in contrast to previously studied sam- CH1 CE1L ple 306a, whose parameters lie in region 2, for which 6 the conduction band bottom is formed by the states of the 3L valleys in the Ge layer.3 It is evident from Fig. 4 CH1 that the relative intensity of the CE cyclotron reso- CE1L 1L 5 nance line of electrons in sample 307a is substantially Ch1 less than those in samples 308b and 309a. In Fig. 5, the parameters of sample 307a lie at the boundary between 4 regions 2 and 3. This means that, according to the calculations performed in [4], the conduction band in sam- CE1L ple 307a has no discontinuity at the heteroboundary. CH1 However, it should be kept in mind that, as was noted in 3

[4], the data presented in Fig. 5 provide only a qualita- Absorption, arb. units tive assessment, because many of the parameters used in the calculations were previously determined with an CE1L Ch1 insufficient accuracy. Nonetheless, it is seen from a CH1 comparison of Figs. 1 and 4 that, unlike the cyclotron CE 2 resonance spectra of samples 308a and 309a, in which 1L the CE1L cyclotron resonance line of electrons is com- Ch1 parable in intensity to the cyclotron resonance lines of CH1 holes, in the spectrum of sample 307a, the CE1L line is 1 hardly distinguishable. This is indirect evidence that the GeSi layers in sample 307a are not good (i.e., deep 051015 20 25 on the kBT scale) quantum wells for electrons. H, kOe Fig. 4. Cyclotron resonance spectra of (1Ð3) sample 307a and (4Ð6) sample 308a. បω = (1) 1.87, (2) 2.22, (3) 2.83, 4. INTERSUBBAND CYCLOTRON (4) 1.67, (5) 2.40, and (6) 2.95 meV. RESONANCE OF HOLES As was noted above, the energies of quantum con- 308a, 308b finement and magnetic quantization are of the same 309a order of magnitude for sample 309a with wide quantum 0.564 307a 3 wells for electrons. For a nonparabolic law of hole dis- 306a persion, the Landau levels of the holes in different 2 quantum-well subbands interact with each other in a 0.562 very complex manner (Fig. 3). However, it should be 1 remembered that, at 4.2 K, only the lower Landau lev- , nm || els of holes in the first quantum-well subband and, pos- a 4 sibly, in the closely spaced second and third subbands 0.560 can be occupied to a large extent. The selection rules 5 [6Ð9] allow cyclotron transitions (in the Faraday configuration) between Landau levels of the same parity 0.558 3 In [2, 6Ð8], the magnetoabsorption under band-gap photoexcita- 0 0.1 0.2 0.30.4 0.5 tion of charge carriers was investigated in samples 259a and 306a ≈ x (dGe 200 Å), whose parameters correspond to region 2 in Fig. 5, and no cyclotron resonance line of 3L electrons was revealed. This can be explained by the fact that, in the range of magnetic Fig. 5. Boundaries of the regions in the (a||, x) plane for fields studied, the magnetic length (200 Å at H = 15 kOe) and the which the lower valleys of the conduction band in pseudo- quantum well width are of the same order of magnitude. There- morphic layers of Ge and Ge Si solid solution (with fore, a variation in the magnetic field leads to a change in the 1 Ð x x electronic spectrum of the Landau levels of 3L electrons from a equal lattice constants a|| in the layer plane) are arranged strictly two-dimensional shape (an infinitely narrow quantum identically with respect to each other (without regard for the quantum confinement) [4]. In regions 2 and 3, the conduc- well), which is characterized by a cyclotron mass of 0.34m0 [12], to a three-dimensional spectrum of the Landau levels with a tion band bottoms are formed by states of the 3L valleys in cyclotron mass of 0.21m0. As a consequence, the resonance the Ge layer and the 1L valleys in the Ge1 Ð xSix layer, absorption line can be smeared over a wide range of magnetic respectively. Symbols indicate the positions of the parame- fields. ters for samples 306a, 307a, 308a, 308b, and 309a.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 134 ALESHKIN et al. (s or a), whose numbers (the first numeral in the level It can be seen from Fig. 2 that the magnetoabsorp- notation) differ by unity (∆n = ±1). Specifically, in the tion spectra of sample 309a contain five resonance lines absence of mixing of states, the matrix elements should (Ch1, Ch3, Ch' , Ci1, Ci2) in the magnetic field range to be maximum for transitions between Landau levels 3 the right of the main cyclotron resonance line CH1 of belonging to the same quantum-well subband and be holes. A detailed analysis of the absorption spectra approximately equal to zero for intersubband transi- (only certain lines observed in this range are shown in tions. Consequently, the cyclotron resonance spectra of Fig. 1) demonstrates that three resonance lines (Ch , holes should contain a limited number of absorption 1 ' lines. Ch3, Ch3 ) can be attributed to the cyclotron resonance of holes. In particular, the Ch1 line, which is observed Let us first analyze the possible transitions from the in magnetic fields of 6 kOe and more (when the inter- lower Landau level 0s1 of holes. It is evident that the action between the levels plays an insignificant role), CH1 line observed at low frequencies can be assigned to can be assigned to the 3a1 4a1 transition. This the 0s1 1s1 transition (see also [6Ð8]). As the assignment is confirmed by the fact that the intensity of energy (magnetic field) increases, the 1s1 level interacts the Ch1 line increases with respect to the intensity of the with the 1s3 level in the third quantum-well subband CH1 line in a weak dc electric field (of the order of sev- and then anticrosses it; in turn, the 1s3 level anticrosses eral V/cm) that leads to heating of charge carriers and, correspondingly, to an increase in the population of the the 1s5 level in the fifth subband (Fig. 3). Upon anti- higher lying Landau level 3a1 as compared to that of the crossing, the 1s1, 1s3, and 1s5 levels “exchange” the wave functions and intensities of the cyclotron transi- 0s1 level (see [6Ð8]). In the case when the photon energy increases above 1 meV, the magnetoabsorption tion from the 0s1 level. With an increase in the photon energy (magnetic field), this exchange should lead to a spectra of sample 309a in magnetic fields of 10–16 kOe contain the higher frequency line Ch3 in addition to the decrease in the intensity of the 0s1 1s1 transition Ch1 line (Fig. 2). Note that the greater the magnetic and an increase in the intensity of the 0s1 1s3 transition and then to a decrease in the intensity of the field strength, the lower the intensity of the former line 0s 1s transition and an increase in the intensity of and the higher the intensity of the latter line. As is seen 1 3 from Fig. 3, it is in this range of magnetic fields that the the 0s1 1s5 transition. This situation is illustrated in 4a level anticrosses the 4a level; as a result, the matrix Fig. 2, which shows the calculated energy positions of 1 3 element of the transition from the 3a1 level to the 4a1 the aforementioned three transitions in the spectral level is transformed into the matrix element of the tran- regions where they occur with a sufficiently high inten- sition from the 3a level to the 4a level. Therefore, the sity. Comparison of the experimental and calculated 1 3 data presented in Fig. 2 allows us to assign the observed Ch3 line can be attributed to the 3a1 4a3 transition. lines CH and CH to the 0s 1s and 0s 1s Moreover, in these magnetic fields, there appears a new 3 5 1 3 1 5 ' transitions, respectively. lower frequency line, namely, Ch3 . Making allowance for the aforesaid, it is reasonable to assign the Ch3' line Now, we consider the resonances observed in the to the 3a3 4a1 transition, because the 4a1 level after absorption spectra in stronger magnetic fields than anticrossing the 4a3 level is characterized primarily by those for the main cyclotron resonance line CH1 of the wave functions corresponding to the third quantum- holes and the cyclotron resonance line CE1L of elec- well subband of holes. trons (Figs. 1, 2). In this range of magnetic fields, the magnetoabsorption spectra of sample 306a with rela- The measurement of the intersubband cyclotron res- tively narrow quantum wells (dGe = 200 Å) and, corre- onance opens the way to a more precise determination spondingly, with a considerable energy separation of the parameters of the Luttinger Hamiltonian for between the hole subbands contain the cyclotron reso- holes in Ge/GeSi quantum-well heterostructures. In [6Ð 8], it was noted that, in quantizing magnetic fields, the nance line of holes with an effective mass of 0.1m0 due to the 3a 4a transition from the lower energy positions of the cyclotron resonance lines of holes 1 1 observed in the spectra of samples with narrow Ge state belonging to the second (a) ladder of the Landau quantum wells correspond to effective masses that are levels [6Ð8]. It can be seen from Fig. 3 that, for sample 10Ð15% larger than the calculated values for the bulk 309a with wide Ge quantum wells, the 3a1 level in parameters of the Luttinger Hamiltonian [10]. This sug- magnetic fields up to 25 kOe strongly interacts with the gests that there is a considerable change in the parame- 3a3 level, anticrosses it, and exhibits a sublinear depen- ters A and D, because the cyclotron mass of holes in dence of the energy of state on the magnetic field. Sim- strained Ge layers is proportional to (A + D/31/2)Ð1 [11]. ilarly, the 4a1 level anticrosses the 4a3 level, which, in The observation of the intersubband cyclotron reso- turn, anticrosses the 4a5 level. This indicates a strong nance makes it possible to determine the parameters A mixing of the 3a1 and 3a3 states and also the 4a1 and 4a3 and D independently. The point is that the quantum- states in magnetic fields beginning with approximately confinement energy, to a first approximation, is propor- 10 kOe. tional to another of their combinations, namely, (A Ð

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 INTERSUBBAND CYCLOTRON RESONANCE OF HOLES 135

1/2 D/3 ), i.e., the reciprocal of the classical hole mass in CH1 the direction perpendicular to the quantum-well plane. 0.30 (‡) The ﬁrst calculations (Fig. 2) demonstrated that the បω = 1.21 meV energy positions of the intersubband cyclotron reso- 0.25 nance lines are highly sensitive to the parameters of the Luttinger Hamiltonian for holes. 0.20 CI1 0.15 Ch 5. IMPURITY MAGNETOABSORPTION 3 1 As can be seen from Fig. 2, the magnetoabsorption 0.10

Absorption, arb. units 2 spectra of sample 309a contain a large number of lines 3 4 that cannot be assigned to the cyclotron resonance of 0.05 holes. In particular, these are the CI1 and CI2 resonance lines, whose positions correspond to extensions of the 0 5 10 15 CH and CH resonance lines (depicted by the solid H, kOe 3 5 I curves in Fig. 2), and the resonance lines observed in (b) CE1L the frequency range below the frequency of the Ch1Ð 0.6 CE1L Ch3' resonances. In our opinion, the majority of these បω = 1.95 meV resonances can be attributed to shallow-impurity- CH assisted transitions. A detailed analysis of the impurity 0.4 3 magnetoabsorption spectra is beyond the scope of this paper (the submillimeter impurity magnetoabsorption 1 ≤ spectra of samples with narrower quantum wells dGe 350 Å were considered in [13, 14]). In our recent work 0.2 2 [9], we proposed a method for calculating the energy Absorption, arb. units spectrum of the impurity states in quantizing magnetic 3 fields, which is based on expanding the wave function 4 of an impurity center in terms of wave functions of the 0510 15 20 25 Landau levels of holes in a quantum well. However, this H, kOe I method proved to be inadequate for describing acceptor CE1L CE1L energy states in sample 309 with wide quantum wells. 1.0 (c) For this sample, it is expedient to analyze the experi- បω = 1.95 meV CH3 mentally observed features in the behavior of different 0.8 lines as a function of the frequency, the applied electric field, and the photoexcitation intensity, which would 1 allow us to judge their impurity origin. A simple tech- 0.6 nique that, in a number of cases, provides a means for 2 separating the cyclotron resonance lines of free carriers 0.4 and the impurity absorption lines is the heating of charge carriers in a dc electric field (see, for example, Absorption, arb. units 0.2 3 [6Ð8]). Figure 6a shows the magnetoabsorption spectra of sample 309a at a photon energy of 1.21 meV in different dc electric fields. It can be seen from this figure 0510 15 20 25 that, as the heating electric fields increases, the inten- H, kOe sity of the CI1 resonance line decreases to the point of disappearance at E = 14 V/cm, whereas the intensity of Fig. 6. Magnetoabsorption spectra of sample 309a in differ- the main cyclotron resonance line CH1 of holes changes ent dc electric fields E and at different intensities of band- gap photoexcitation. (a) E = (1) 0, (2) 6.8, (3) 14, and to a considerably lesser extent. Hence, there are (4) 26 V/cm; photoexcitation with a low intensity. (b) E = grounds to believe that the CI1 resonance line is associ- (1) 0, (2) 6.8, (3) 14, and (4) 16 V/cm; photoexcitation with ated with the transitions between impurity states, the a low intensity. (c) E = 0, the photoexcitation intensity lower of which is depleted in response to a dc electric increases in order of increasing curve number. field, for example, due to impact ionization. However, quite a different situation is observed in the magnetoabsorption spectra measured at a photon energy of fields; furthermore, the intensity of the CH3 line initially even increases with an increase in the electric 1.95 meV (Fig. 6b). In this case, the CH3 resonance line, which, according to the data presented in Fig. 2, field. This fact not only counts in favor of the assump- should gradually transform into the CI1 line, is retained tion that the CI1 and CH3 resonance lines have different in the spectra over the entire range of heating electric origins but also confirms our assignment of the CH3

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 136 ALESHKIN et al. line to the intersubband cyclotron resonance of holes at photon energies ranging from 0.5 to 1.3 meV. This due to the 0s1 1s3 transition. Indeed, our calcula- line cannot be assigned to the cyclotron resonance of tions demonstrate (Figs. 2, 3) that, at a photon energy holes, because no allowed transitions (satisfying the of the order of 2 meV, the cyclotron transitions from the condition ∆n = ±1) from the lower (occupied) Landau 0s1 level to the 1s1 level and, then, to the 1s3 level occur levels occur in the range 6Ð24 kOe at such low energies to the states lying above the point of their anticrossing. (see Fig. 3). As can also be seen from Fig. 2, the slope Therefore, the maximum oscillator strength corre- of the magnetic-field dependence of the resonance fre- sponds to the transition to the third subband and the quency for the Ci1 line is almost identical to that for the CH resonance line associated with the weaker transi- 1 Ch1, Ch3, and Ch3' lines and is severalfold smaller than tion becomes difficult to distinguish from the back- the slopes for the CH , CH , CH , CI , and CI lines. ground of the CE cyclotron resonance line of elec- 1 3 5 1 2 1L Therefore, we can assume that the Ci line is associated trons. 1 with the transition between two shallow acceptor states I 4 belonging to 3a and 4a Landau levels. Since the Ch1 Although the CE1L resonance line is dominant in the magnetoabsorption spectra depicted in Fig. 6b, the line in Fig. 2 is located below the Ci1, Ch3, and Ch3' data on its energy positions are not presented in Fig. 2. cyclotron resonance lines, it is quite possible that the We succeeded in revealing this line in the study of the given transition occurs from a shallow impurity state at magnetoabsorption at different intensities of band-gap the 3a Landau level to a deeper lying impurity state at photoexcitation in combination with dc heating of the 4a Landau level. In the case of hydrogen-like I donors in GaAs/AlGaAs heterostructures, the 2p charge carriers (Figs. 6b, 6c). The CE1L line is Ð observed against the background of the cyclotron reso- 2s transition is an analog of the aforementioned transi- nance line of 1L electrons only at a low intensity of tion. In a strong magnetic field, the 2pÐ level corre- band-gap photoexcitation. An increase in the electric sponds to an excited state of the Coulomb center at the field leads to a drastic decrease in the intensity of the Landau level n = 0, whereas the 2s state is the ground I (and, hence, deeper) state at the Landau level n = 1 (see, CE1L line as compared to the intensity of the CE1L for example, [15]). cyclotron resonance line of electrons. According to the I results of polarization measurements, the CE1L line corresponds to the electron circular polarization of ACKNOWLEDGMENTS radiation. Therefore, the new line can be attributed to We would like to thank M.D. Moldavskaya for long- the transitions between shallow excited states (∆E ≈ term cooperation laying the groundwork for the present 0.17 meV) of residual donors. In an applied electric study, E.A. Uskova for preparing the samples use in our field, these states are depleted and the intensity of the measurements, V.L. Vaks and A.N. Panin for their assis- I tance in performing the experiments with backward- CE1L impurity line decreases, as is the case with acceptors. The influence of the band-gap photoexcita- wave tubes, and Yu.N. Drozdov for x-ray diffraction tion intensity on the relative population of the donor investigations of the samples. levels and Landau levels of 1L electrons is illustrated in This work was supported by the Russian Foundation Fig. 6c. At low excitation intensities, the charge carriers for Basic Research (project no. 03-02-16808) and the are predominantly captured by ionized impurity centers Russian Federal program “Integration” (project and the fraction of free electrons is small. In this case, no. B0039/2102). I the CE1L line is dominant in the magnetoabsorption spectrum (Figs. 6b, 6c). An increase in the intensity of REFERENCES the band-gap photoexcitation is accompanied by an increase in the intensity of the CE1L cyclotron reso- 1. L. K. Orlov, O. A. Kuznetsov, R. A. Rubtsova, et al., nance line of electrons, which, in turn, leads to a con- Solid State Phenom. 32Ð33, 469 (1993). siderable shift of the total absorption line (Fig. 6c). 2. V. I. Gavrilenko, I. N. Kozlov, O. A. Kuznetsov, et al., Pis’ma Zh. Éksp. Teor. Fiz. 59 (5), 327 (1994) [JETP As was already noted, the Ch1, Ch3, and Ch3' cyclo- Lett. 59, 348 (1994)]. tron resonance lines are attributed to the transitions 3. C. M. Engelhardt, D. Tobben, M. Ashauer, et al., Solid- between the Landau levels 3a1 4a1, 3a1 4a3, State Electron. 37, 949 (1994). and 3a3 4a1, respectively. These lines are observed 4. V. Ya. Aleshkin and N. A. Bekin, Fiz. Tekh. Polupro- in the frequency range below the frequency corre- vodn. (St. Petersburg) 31 (2), 171 (1997) [Semiconduc- sponding to the main cyclotron resonance line CH1 of tors 31, 132 (1997)]. holes. It can be seen from Figs. 2 and 3 that, in this 4 range, there are several more low-frequency absorption We deliberately do not specify the indices characterizing the number of the quantum-well subband, because, in this range of lines, the most intense of which is the Ci1 line observed magnetic fields, the 3a and 4a states in the first and third sub- over a wide range of magnetic fields from 6 to 24 kOe bands undergo strong hybridization (Fig. 3).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 INTERSUBBAND CYCLOTRON RESONANCE OF HOLES 137

5. V. I. Gavrilenko, I. V. Erofeeva, A. L. Korotkov, et al., 11. G. L. Bir and G. E. Pikus, Symmetry and Stain-Induced Pis’ma Zh. Éksp. Teor. Fiz. 65 (2), 194 (1997) [JETP Effects in Semiconductors (Nauka, Moscow, 1972; Lett. 65, 209 (1997)]. Wiley, New York, 1975). 6. V. Ya. Aleshkin, V. I. Gavrilenko, I. V. Erofeeva, et al., in 12. F. Stern and W. E. Howard, Phys. Rev. 163 (3), 816 Proceedings of the Workshop on Nanophotonics (IFM (1967). Ross. Akad. Nauk, Nizhni Novgorod, 1999), p. 114. 13. V. Ya. Aleshkin, A. V. Antonov, D. B. Veksler, et al., in 7. V. Ya. Aleshkin, V. I. Gavrilenko, I. V. Erofeeva, et al., in Proceedings of the Workshop on Nanophotonics (IFM Proceedings of the 6th International Symposium “Nano- Ross. Akad. Nauk, Nizhni Novgorod, 2003), p. 248. structures: Physics and Technology,” St. Petersburg, 14. V. Ya. Aleshkin, D. B. Veksler, V. I. Gavrilenko, et al., Russia (1999), p. 356. Fiz. Tverd. Tela (St. Petersburg) 46 (1), 126 (2004) 8. V. Ya. Aleshkin, V. L. Vaks, D. B. Veksler, et al., Izv. [Phys. Solid State 46, 125 (2004)]. Akad. Nauk, Ser. Fiz. 64, 308 (2000). 15. S. R. Ryu, Z. X. Jiang, W. J. Li, et al., Phys. Rev. B 54 9. V. Ya. Aleshkin, V. I. Gavrilenko, D. B. Veksler, and (16), R11086 (1996). L. Reggiani, Phys. Rev. B 66, 155336 (2002). 10. J. C. Hensel and K. Suzuki, Phys. Rev. B 9 (10), 4219 (1974). Translated by O. Borovik-Romanova

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 138Ð145. From Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 138Ð145. Original English Text Copyright © 2004 by Lusakowski, Knap, Dyakonova, Kaminska, Piotrowska, Golaszewska, Shur, Smirnov, Gavrilenko, Antonov, Morozov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Magnetotransport Characterization of THz Detectors Based on Plasma Oscillations in Submicron Field-Effect Transistors* J. Lusakowski1, 2, W. Knap1, 3, N. Dyakonova1, E. Kaminska4, A. Piotrowska4, K. Golaszewska4, M. S. Shur3, D. Smirnov5, V. Gavrilenko6, A. Antonov6, and S. Morozov6 1 GES–UMR, CNRS–Université Montpellier 2, Montpellier, 34950 France 2 Institute of Experimental Physics, University of Warsaw, Warsaw, 00-681 Poland 3 Rensselaer Polytechnic Institute, Troy, New York, 121180-3590 USA 4 Institute of Electron Technology, Warsaw, 02-668 Poland 5 Ioffe Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia 6 Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected]

Abstract—Magnetotransport characterization of field-effect transistors in view of their application as resonant detectors of THz radiation is presented. Three groups of different transistors based on GaAs/GaAlAs or GaInAs/AlGaAs heterostructures are investigated at liquid–helium temperatures and for magnetic fields of up to 14 T. The magnetic-field dependence of the transistor resistance is used for evaluation of the electron density and mobility in the transistor channel. The electron mobility and concentration determined from magnetotransport measurements are used for the interpretation of recently observed resonant detection of terahertz radiation in 0.15 µm gate length GaAs transistors and for the determination of the parameters of other field-effect transistors processed for resonant and voltage tunable detection of THz radiation. © 2004 MAIK “Nauka/Interpe- riodica”.

* 1. INTRODUCTION netic field which tuned the energy of optical transitions between the levels of shallow donors or cyclotron and The terahertz part of the electromagnetic spectrum impurity-shifted cyclotron resonance. Such detectors, lies at the border between wavelengths generated by however, require liquid-helium temperatures and mag- solid-state electronics and optics. Many excitations netic fields of a few tesla. observed in condensed matter, liquids, gases, and biological substances correspond to the THz range of fre- For many applications, tuning the response of a quencies, i.e., to photon energies of ~0.3Ð30 meV. detector using an applied voltage is much easier than Spectral analysis in the THz region can be used for using a magnetic field. A resonant, voltage-tunable studies of these excitations, such as phonons, cyclotron detection based on excitation of plasmon resonance in or spin resonance, as well as for investigations of a two-dimensional electron gas (2DEG) confined in a molecular (rotational and vibrational) excitations in field-effect transistor (FET) was proposed in the early liquids, gases, and biological substances. The growing 1990s [11, 12] and reported only recently [13Ð15]. A interest in the analysis of signals carried by THz radia- FET, biased by a gate-to-source voltage Ugs and subject tion is also related to possible applications of THz spec- to electromagnetic radiation, can develop a constant troscopy for nondestructive sensing and imaging in drain-to-source voltage Uds, which has a resonant medicine, the food industry, and defense [1, 2]. dependence on the frequency of radiation with maxima ω π Terahertz broadband detectors include bolometers at plasma oscillation frequencies [12], fN = N/2 . Res- onant plasma frequencies are discrete and given by [3Ð5], pyroelectric detectors, Schottky diodes [6, 7], ω ω ω π and photoconductive detectors [8]. An advantage of N = 0(1 + 2N), where 0 = s/2L and N = 0, 1, 2, …. selective and tunable detectors is that they require no The plasma wave velocity s depends on the carrier den- gratings of moving mirrors to perform a spectral analy- sity in the transistor channel n and the gate-to-channel εε 2 1/2 sis. Tunability was demonstrated for photoconductive capacitance (C = 0/d) per unit area: s = (e n/mC) , detectors (GaAs [9], InP [10], InSb) placed in a mag- where e and m are the electron charge and the effective mass, respectively; ε is the dielectric constant; and d is *This article was submitted by the authors in English. the gate-to-channel distance. In the gradual channel

MAGNETOTRANSPORT CHARACTERIZATION OF THz DETECTORS 139 approximation, the carrier density in the channel is 60 related to the gate-to-source voltage by the relation n = 1.5 CU0/e, where U0 is the gate-to-channel voltage swing, 50 Light on U = U Ð U , and U is the threshold voltage. The fun- 0 gs th th 1.0 damental plasma frequency can be expressed by an 40 approximate relation, , arb. units sd

30 U 0.5 Dark 1 eU f = ------0 . (1) 0 0 4L m 20 –0.4 –0.3 –0.2 This has two important consequences: (i) a sufﬁ- Ug, mV

Source–drain voltage, mV 10 ciently short (submicron) FET can operate as a THz detector and (ii) the response frequency of such a detec- 0 tor can be tuned using a gate-to-source voltage. –600–400 –200 0 The width of a resonant curve is determined by the Gate voltage, mV quality factor ω τ, where τ is the electron-momentum 0 Fig. 1. Photoinduced drain-to-source voltage of relaxation time. Resonant detection becomes possible GaAs/GaAlAs FET (from group A) as a function of gate-to- if the quality factor reaches and exceeds a value of 1. If source voltage and temperature from 8, 20, 60, and 100 K ω τ Ӷ 0 1, plasma oscillations are overdamped and the to 200 K (from top to bottom). Inset shows the resonant FET response is a smooth function of ω, as well as of detection of the 0.6, 0.8, and 1.2 THz radiation from multiplied Gunn diode source (for details, see [13, 16]). Higher gate-to-source voltage (nonresonant broadband detec- Gunn diode harmonics are visible after illumination of FET tion [16]). [14]. The arrows mark positions of 2D plasmon resonances and correspond to detection of 0.6, 0.8, and 1.2 THz from Resonant and nonresonant detection of THz radia- left to right correspondingly (for details, see [13, 14]). tion was recently demonstrated in two field-effect devices: a commercial FET [13, 14, 16] and a double quantum well FET with a periodic grating [16]. In both device. The magnetotransport determination of these cases, the frequency of a standing 2D plasmon wave parameters is addressed in the present work. was tuned to a THz frequency by varying the gate-to- The standard equations for the current density ( j) in source voltage. In Fig. 1, we show an example of the the 2DEG in the presence of a magnetic field (perpen- resonant detection of THz radiation performed using a dicular to the 2DEG plane) are GaAs/GaAlAs FET. j = σ E + σ E , The temperature evolution of spectra shown in x xx x xy y Fig. 1 is mainly related to a change in the electron scat- j = Ðσ E + σ E . tering time. A resonant feature (marked by an arrow) y xy x xx y starts to become visible below about 30 K because only Here, Ex and Ey are the components of the electric field σ σ then does the electron scattering time increase suffi- in the (xy) plane and xx and xy are components of the ω τ ӷ ciently for the condition 0 1 to be fulfilled. Illumi- conductivity tensor. In the DrudeÐBoltzmann theory, nation of the transistor with visible light leads to an these components depend on the magnetic field: additional increase in the electron mobility (µ) and, as ω τ σ = σ /1()+ µ2 B2 , a result, to an increase in the quality factor 0 . This xx 0 allowed for better resolution of the main resonance σ σ µ ()µ2 2 (0.6 THz) and observation of the resonant detection of xy = 0 B/1+ B . higher harmonics (0.8 and 1.2 THz) of a frequency- The boundary conditions for these equations depend multiplied 0.2 THz Gunn diode source, as shown in the on the sample geometry. Two important limiting cases inset to Fig. 1. considered in this work are the Hall bar geometry and The most important parameters related to the reso- “transistor geometry” (with the device width D being nant detection are the electron scattering time and the much larger than the device length L). For a long Hall electron concentration. The former, related to the elec- bar, L ӷ D. In this case, there is no current in the “y” ω τ σ tron mobility, enters into the quality factor 0 , which, direction, jy = 0, and the measured Ex = jx/ 0. This for a given value of τ, gives a low bound of frequency means that conductivity (and resistivity) does not for which FET can operate as a resonant detector. The depend on the magnetic field. In other words, there is electron concentration determines the transistor thresh- no magnetoresistance. This is a general feature of a old voltage (which affects the maximum swing voltage degenerate two-dimensional gas. On the other hand, in directly related to the frequency of plasmon resonance, the case of a very short but wide device (L Ӷ D), the as shown in Eq. (1)). Therefore, determination of the Hall voltage is short-circuited by long current-supply- σ electron density and mobility in a transistor is a key ing contacts. Then, Ey = 0 and jx = xxEx. This geometry point in view of its applications as a resonant plasma is equivalent to that of the Corbino disk. In this case, the

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 140 LUSAKOWSKI et al.

100

200 A

80 µ , d

I 100 60 A

µ 0 5 10 15 20 , d I 40 UD–S, mV T5 (4.2 K) 20

0 –0.5–0.4 –0.3 –0.2 –0.1 0 UG–S, V

Fig. 3. Example of the characteristics of transistor T5 (from group B). Transient characteristics at T = 4.2 K as a function of the magnetic ﬁeld B equal to (from top to bottom) 0, Fig. 2. Photograph of a dice of the group B and C devices 0.030, 0.051, 0.068, 0.090, 0.140, 0.260, and 1 T. The inset with six lithographically deﬁned transistors, two Hall bars, shows output characteristics for gate-source voltage equal and a Schottky diode. to (from top to bottom) 0, Ð0.1, Ð0.2, Ð0.3, and Ð0.4 V.

µ2 2 σ measured Ex = jx(1 + B )/ 0 and one expects a para- GaAs/GaAlAs and GaInAs/GaAlAs heterostructures, bolic increase in the sample resistance and a Lorentzian respectively. The group B transistors had a threshold (1/(1 + µ2B2)) decrease in the conductance. The coeffi- voltage of Ð0.2 to Ð0.5 V and an electron mobility of 5Ð cient of the parabolic magnetoresistance (or half-width 20 m2/Vs at 4.2 K, while the corresponding values for or Lorentzian magnetoconductivity) is equal to the the group C transistors were Ð1 to Ð2 V and 1Ð2 m2/Vs, mobility. In quantizing magnetic fields (µB ӷ 1), the respectively. The gate-to-channel distance was d ~ 160 conductivity exhibits ShubnikovÐde Haas oscillations. and 40 nm for group B and C transistors, respectively. These oscillations are periodic as a function of inverse The same mask was used in the case of B and C (Fig. magnetic field (1/B), the period depending only on the 2), which defined transistors with a gate length equal to carrier density. 0.8, 1.5, and 2.5 µm. The source-to-drain distance was µ In this work, different GaAs and GaInAs FETs and 10 m for all transistors, and the gate was placed close Hall-bar test structures were investigated using magne- to the source contact to ensure asymmetry of the tran- totransport measurements in high magnetic fields (up to sistor (necessary for the detection). Two gated Hall bars 14 T). We show how magnetoconductivity data make it and a Schottky diode were fabricated next to each possible to evaluate the electron mobility and concen- group of the six transistors. Hall structures were used tration in a transistor channel even for a nonideal geom- for independent measurements of the electron density etry. The results are then used to interpret the recently and mobility. observed resonant detection and to estimate the param- Measurements were carried out at liquid-helium eters relevant to the THz detection in these field-effect temperatures (4.2 or 8 K) after cooling the sample in transistors. The maximum frequency and the quality the dark. A typical set of measurements carried out on factor that limit the THz detection in different field- transistors involved the following: (i) output character- effect structures are discussed. istics (drain current Id vs drain-to-source voltage Uds) as a function of Ugs voltage and magnetic field B; (ii) transient characteristics (drain current vs gate-to-source 2. EXPERIMENT AND RESULTS voltage Ugs) as a function of B; and (iii) magnetocon- Three groups of devices, named A, B, and C, were ductivity (drain current vs B) as a function of gate-to- investigated. Group A included commercially available source voltage. (Let us note that, in the following, the Fujitsu FX20 FETs with a gate length (L) of 0.15 µm, gate-to-source voltage is always negative and its gate width (D) of 50 µm, and gate-to-channel separa- increase means an increase in its absolute value.) An tion (d) of ~25 nm. Their threshold voltage varied example of the experimental data for one of the group between Ð0.2 and Ð0.5 V, and the electron mobility was B transistors is shown in Fig. 3. estimated to be 0.1Ð0.2 m2/Vs at 300 K and 0.5Ð In some cases, additional data were taken after illu- 1.0 m2/Vs at 4 K. mination of a sample with a red lightÐemitting diode. Transistors and Hall bars of groups B and C were Output characteristics were used to determine the range processed out of MBE-grown high-electron-mobility Uds and Ugs which the drain current changed linearly

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 MAGNETOTRANSPORT CHARACTERIZATION OF THz DETECTORS 141

80 1.0 1.0 (0) 1.0 σ 1/2 )/

0.8 B 0.8 ( 0.8 σ 60 (0) 0.6 σ 0.6 = 1 T)] )/ B B

0.4 ( ( 0.6 0.4 R (0) σ ∆ R 0.2 /

)/ 40

R 0.2 B ∆ (

0.4 [

R 0 2 46 B, T 0 0.2 0.40.6 0.8 1.0 20 0.2 B, T Normalized conductivity 0 2 4 6 8 10 12 14 00.2 0.4 0.6 0.8 1.0 B, T B, T Fig. 5. Influence of the magnetic field on conductivity for transistor T3 (upper line) and T5 (lower line); both transis- Fig. 4. The resistance of a group A transistor, normalized at tors are from group B. The inset shows a square root of mag- zero magnetic field, for Ugs = 0, 0.2, and 0.3 V (from top to netoresistance R = R(B) Ð R(0) of transistors T3 and T5 nor- bottom). The inset shows normalized Lorentzian magneto- malized to its value at 1 T. The curves correspond to a gate- conductivity σ(B) curves characterized by decreasing µ for to-source voltage equal (in volts) of 0, Ð0.1, Ð0.2, Ð0.3, and increasing Ugs. Ð0.4 for T5 and 0, Ð0.1, Ð0.2, and Ð0.3 for T3. with drain-to-source voltage. Transient characteristics channel. The carrier density obtained from these oscil- allowed determination of the threshold voltage, the val- lations (equal to 1.9 × 1012 cmÐ2) is expected to corre- ues of which are cited in the preceding paragraph. late with the carrier density in the transistor channel at zero gate voltage. (It might be somewhat different The analysis of the magnetoconductivity of transis- depending on the values of the surface potential and of tors presented below uses the following scheme. At low the gate contact built-in voltage.) magnetic fields, one observes a strong decrease in conductivity with an increase in the magnetic field, which Let us concentrate now on measurements carried leads to a Lorentz-like shape of the magnetoconductiv- out on two transistors (T3 and T5 from group B). The ity curve. This curve is used to estimate the electron transistors differed in the length of the gate and the lat- mobility in the transistor channel. At large magnetic eral dimension, which were equal to 2.5 and 55 µm for fields, ShubnikovÐde Haas oscillations are observed T3 and 1.5 and 25 µm for T5, respectively. and used to determine the electron concentration. Mea- Figure 5 shows the normalized magnetoconductiv- surements were performed for different values of the ity for transistors T3 and T5 for zero gate-to-source gate-to-source voltage. Results of measurements car- voltage. Lorentz-like curves show a strong decrease in ried out on transistors are compared with magne- the drain-to-source conductivity σ with an increase in totransport results obtained for gated Hall bars. the magnetic field. Curves of a similar shape were Figure 4 shows an example of a normalized drain- obtained for all gate-to-source voltages; they differ to-source resistance of a group A transistor versus the only in their half-width. The shape of the magnetocon- magnetic field for a few values of the gate-to-source ductivity curves is not strictly Lorentzian, in contrast to voltage. A background of these curves was fitted up to the curves shown in the inset to Fig. 4. This is illus- 4 T with a very high accuracy by a parabolic depen- trated in the inset to Fig. 5, which shows the square root dence, 1 + µ3B2, with the mobility µ as a single fit of a transistor magnetoresistance [R(B) Ð R(0)]1/2 nor- parameter. We obtained µ equal to 0.60, 0.38, and malized to its value at 1 T. If the magnetoconductivity 2 2 Ð1 0.17 m /Vs for Ugs equal to 0, Ð0.2, and Ð0.3 V, respec- were to be described by a Lorentzian (1 + (B/B1/2) ) , tively. This decrease in µ corresponds to the broadening then this figure would show a straight line. We found of Lorentzian curves shown in the inset to Fig. 4, which that the magnetoresistance for all gate-to-source volt- present the magnetoconductivity σ(B) normalized to its ages and for both transistors can be described by a value at B = 0 T. The half-width of each Lorentzian, Lorentzian-like dependence but with the exponent µÐ1 equal to 1.3 rather than 2. The inverse of the half-width B1/2, is given, of course, by an appropriate value of . A simple inspection of the ShubnikovÐde Haas oscilla- of these Lorentzian-like magnetoconductivity curves, Ð1 tions in Fig. 4 shows that the number and position of B1/2 , is plotted as a function of the gate-to-source volt- maxima do not change with the applied gate-to-source Ð1 voltage, which means that, in this transistor, they are age in Fig. 6. This parameter, B1/2 , of a dimension of mainly due to the ungated part of the source-drain mobility decreases with increasing gate-to-source volt-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 142 LUSAKOWSKI et al. to a difference in the sample geometry, which is Corb- 20 ino-like for the case of the transistors. Gated Hall-bar structures placed close to the transistors were used to 16 perform a precise analysis of the inﬂuence of the gate- to-source voltage on the electron mobility and concentration in heterostructures used for transistor fabrica- /V s 12 2 tion. In Fig. 8, we show examples of results obtained on

, m one of the Hall bars placed together with the group (C, –1 1/2 8 GaAs/GaInAs heterostructure). Figure 8 shows the B resistance values measured between the Hall-bar 4 probes as a function of the magnetic ﬁeld. The curves were normalized to their value at B = 0 T, and mono- 0 tonic background magnetoresistance was subtracted for –0.5 –0.4 –0.3 –0.2 –0.1 0 better visualization. Typical ShubnikovÐde Haas oscil- Ð1 UG–S, V lations were observed. The period (in B ) of the oscillations changes with decreasing the gate-to-source volt- Fig. 6. Inverse of the half-width of magnetoconductivity age swing, which corresponds to a decrease in the elec- Ð1 µ tron concentration. It is important to note, however, that curves B1/2 for transistors T5 (L = 1.5 m, down triangles) and T3 (L = 2.5 µm, solid circles) as a function of gate-to- not only the carrier density but also the mobility source voltage Ugs. changes with increasing gate voltage; the amplitude of oscillation decreases, and, close to the threshold, they are practically smeared out. 1

(0) Figure 9 summarizes the mobility and carrier den- σ

)/ sity measurement results. As expected, the carrier den- B

( sity decreases linearly with the application of a nega- σ tive gate voltage. The linear extrapolation of the density 0.1 versus gate voltage dependence to zero sheet density yields a threshold voltage equal to Uth = Ð1.6 V. The threshold voltage obtained in this way is different from the “transistor threshold” voltage; this point will be dis- 0.01 T3 cussed later. The mobility ﬁrst increases slightly and then rapidly decreases with the gate voltage swing. T5 Typically, we observed a mobility decrease by a factor of 2 to 3 at a gate voltage equal to half of the threshold Normalized conductivity 0 1 2 3 4 5 6 7 voltage. B, T

Fig. 7. Magnetoconductance of transistors T3 (upper curve) 3. DISCUSSION and T5 (lower curve). The following discussion is divided into two parts. First, we consider the possibility of evaluating the elec- age for transistor T5 (expect for a very small increase at tron concentration and mobility in the transistor channel based on magnetoconductivity measurements. In the lowest Ugs) and shows a minimum for transistor T5. The curves shown in Fig. 6 coincide for U < Ð0.3, view of this, we discuss the influence of the geometry gs of the investigated structures on the result of such a pro- which, for both transistors, corresponds to a drain cur- cedure. Also, the influence of the gate potential on the rent of about 20% of its value at the zero gate-to-source carrier density and mobility in transistors and Hall bars voltage. is discussed. Second, the electron mobility and concen- Figure 7 compares the conductivity of transistors T3 tration determined from magnetotransport measure- and T5 (measured at Ugs = 0 V) as function of the mag- ments are used for the interpretation of recently netic field up to 7 T. After Lorentz-like behavior at low observed resonant detection and determination of the fields, oscillations in the conductivity were observed. parameters of new field-effect transistors processed for Taking into account the positions of minima of the resonant detection of THz radiation. magnetoconductance data, one can evaluate a concen- The magnetoresistance measured between the tration of the 2DEG, which appears to be 3.0 × 1011 and source and the drain of the transistor is an integral phe- 3.2 × 1011 cmÐ2 for transistors T3 and T5, respectively. nomenon because of two effects: (i) it comprises con- One can note that the oscillations on the magnetocon- tributions from both the gated and ungated part of a ductance curves are different from the usual traces transistor channel and (ii) the channel geometry is often observed in quantum Hall experiments. This is related intermediate between Corbino- and Hall-bar-like.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 MAGNETOTRANSPORT CHARACTERIZATION OF THz DETECTORS 143

The gated part of the channel (gate length) was 1.2 0.15 µm for the group A devices and 0.8Ð2.5 µm for –1 V others. The total channel length was around 1 µm for 1.0 group A devices and 10 µm for groups B and C. Clear evidence of the importance of the ungated part of the –0.6 V channel can be seen in Fig. 4, which shows ShubnikovÐ (0) 0.6 R

de Haas oscillations of the group A transistor. One can )/ –0.4 V B see that the positions of maxima/minima do not depend ( R on the gate-to-source voltage but the resistance of the 0.2 transistor quickly grows with Ugs. This is because the Ug = 0 V oscillations come mainly from the 2D electron gas con- 0 ﬁned in the ungated part of the transistor. The back- –0.2 ground changes, however, because the total resistance increases due to the modulation of the transistor chan- 071 2 3 4 5 6 nel by the gate voltage. B, T

The mobility µ, determined as a coefficient of the Fig. 8. ShubnikovÐde Haas oscillations of magnetoresis- parabolic dependence of resistance, corresponds to an tance of a Hall bar processed out of a GaInAs/GaAlAs het- “average” mobility in the entire region between the erostructure (group C devices) as a function of the magnetic field for a gate potential equal to 0, 0.4, 0.6, and 1 V (from source and the drain. For the zero gate voltage, the car- bottom to top). The curves are normalized at B = 0 T and rier densities in the gated and ungated regions of the shifted vertically for better visualization. channel are nearly the same. However, as is clearly demonstrated by measurements on the gated Hall bars (where the whole conducting region is gated), a gate potential decreases both the mobility and the concen- 1.50 2.5 tration of electrons (Fig. 9). We also expect that the mobilities in the gated and ungated sections of the device are close at zero gate bias, even though the scat- 1.25 2.0 tering in the device channel might be affected by the –2 /V s cm effects related to the metal gate [17]. Once the gate 2 1.00 1.5 voltage is applied, the mobility under the gate is differ- 12 , m µ ent from the measured averaged mobility, since mobil- , 10 ity is a strong function of electron sheet density. With 0.75 1.0 n decreasing gate voltage swing, the resistance of the gated region starts to dominate the total transistor resis- 0.50 0.5 tance. In this case, the measured (average) mobility –1.0 –0.8 –0.6 –0.4 –0.2 0 approaches the value of mobility under the gate. There- U , V fore, the measurements of the magnetoresistance of the G–S channel allow relatively accurate determination of the Fig. 9. The electron mobility (squares) and concentration mobility in the gated region for small gate voltage (down triangles) determined from measurements of the Hall swings. In the intermediate region, one obtains the effect on a gated Hall bar of a GaInAs/GaAlAs heterostruc- approximate “average” mobility. Comparison of Fig. 6 ture from group C. with Fig. 9 shows, however, that the overall functional dependences of the mobility versus gate voltage in the µ µ transistor channel and in the gated Hall bar are similar. that have a very short (Lc ~ 1 m) and wide (d ~ 50 m) The mobility decreases by a factor of 2Ð3 at half the channel. threshold voltage. For transistors T3 and T5, the D/Lc ratio is 5.5 and Another point to be discussed is the conducting 2.5, respectively, and the geometry is neither Corbino channel geometry. As mentioned in the Section 1, the nor a Hall-bar type. We speculate that the observed interpretation of the transistor magnetoresistance is exponent of 1.3 is related to the fact that the geometry simple if the conducting channel geometry approaches of the current flow is far from the ideal cases presented above. In particular, an essential part of the current may the limiting case of the Corbino geometry. This condi- flow outside of the transistor due to violation of the con- tion is fulfilled for a “very wide channel,” with the dition j = 0. Nevertheless, and in spite of above-men- source-to-drain separation length I being much smaller y c tioned difficulties in the interpretation, one can con- than the channel width D. In this case, the magnetore- Ð1 sistance is parabolic (or the magnetoconductance is sider the parameter B1/2 as an estimate of the electron Lorentzian). Such a parabolic (R ~ 1 + µ2B2) behavior mobility. This interpretation is consistent with the was observed for group A transistors (gate of 0.15 µm) behavior of the two curves shown in Fig. 6, which coin-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 144 LUSAKOWSKI et al.

2.0 dence shown in Fig. 9, we obtained a threshold voltage (a) (voltage for which the carrier density is zero) equal to 1.5 A Uth = Ð1.6 V. If we use the same procedure for conduc- 1.0 B&C tivity, a threshold voltage of Uth = Ð1.4 V is obtained. 0.5 This is because both the carrier density and mobility enter into the conductivity and both decrease with an Frequency, THz increase in the gate voltage. It is important to note that 0 0.5 1.0 1.5 the threshold in estimations of the plasma wave fre- 12 (b) quency is the carrier density threshold. 10 B Using the value of the mobility and the threshold 8 voltage determined for different FETs, we can estimate 6 A 4 their parameters for possible applications in resonant C Quality factor 2 detectors of terahertz radiation. In Fig. 10, we show the frequency of the resonant detection and the quality fac- 0 0.5 1.0 1.5 tor as a function of the swing voltage. The maximum Swing voltage, V frequency for a detector is determined by the maximum gate voltage swing and the gate length. As discussed Fig. 10. (a) Frequency of the resonant detection of the group before, the maximum gate voltage swing is determined A, B, and C transistors as a function of the swing voltage; by “the carrier density threshold voltage;” it is usually (b) quality factor corresponding to a frequency of the resonant detection plotted in (a) for the group A, B, and C tran- slightly more negative than the transistor threshold sistors. voltage. The maximum gate voltage swing is about 0.5 V for the group A and B transistors and 1.5 V for the group C transistors. We took a gate length L = 0.15 µm cide for higher gate-to-source voltage, close to the for group A and L = 0.8 µm (shortest gates on a dice) for threshold value (Ugs < Ð0.3 V), when the transistor groups B and C. The mobility was assumed to be 6, 14, resistance is determined by the gated section. The fact and 1 m2/Vs for groups A, B, and C, respectively. that we find the same exponent (equal to 1.3) for both As can be seen from the figure, the maximum fre- transistors confirms that, although determination of the quency of the group A devices is approximately Ð1 electron mobility as B1/2 is an approximation, it can be 1.5 THz. The points shown in Fig. 10 represent the used to compare the electron mobility in different tran- results of recent experiments [13, 14]. The plasma res- sistors. onance observed in the experiments was relatively weak (Fig. 1). This can be understood by looking at the It is important to note that both the mobility figure presenting the quality factor. One can see that the obtained on gated Hall bars (shown in Fig. 9) and the maximum quality factor that can be obtained for these Ð1 devices is around 1.5. The reason for this is the rela- mobility extracted using B1/2 values for the transistors (shown in Fig. 6) decrease as the gate-to-source voltage tively low mobility. For group C, the maximum fre- swing decreases. This might be linked to the screening quency is 0.6 THz. The maximum quality factor for this effects, which diminish at smaller electron sheet densi- frequency is relatively small, equal to about 2. This ties. This decrease reduces the effectiveness of screen- means that these devices cannot be used for resonant ing of ionized centers and results in a decrease in tunable detection. The best quality factors were mobility. The application of the gate voltage also obtained for group B transistors. At the maximum oper- changes the shape of the quantum well at the heteroint- ation frequency of 0.35 THz (corresponding to the erface. The quantum well is wider at smaller sheet den- maximal swing voltage of 0.5 V), the quality factor for sities. Hence, the peak of the 2D electron wave function these devices is larger than 10. These are the most is further away from the heterointerface, which promising devices for high-quality resonant plasma decreases scattering by the interface roughness. This detectors. effect can lead to an increase in mobility. It is possible In principle, the simplest way to increase the maxi- Ð1 mum frequency (and the quality factor) is to decrease that the nonmonotonic behavior of B1/2 observed for the gate length (L) (see Eq. (1)). The shortest gate both transistors (close to zero gate-to-source voltage for length (L ) for a given type of device can be defined T5 and at about Ð0.2 V for T3) and for the Hall bar at min by an approximate relation Lmin ~ 5d, where d is the around Ð0.4 V can be attributed to the interplay of these gate-to-channel distance (in order to preserve the gate two mechanisms. control). Looking at the dimensions of the three groups Measurements of the carrier density and mobility of devices, one can see that the devices of groups A made on the gated Hall bars also show that the thresh- (d ~ 0.025 µm, L ~ 0.15 µm) and B (d ~ 0.16 µm, L ~ old voltage for the carrier density and for the channel 0.8 µm) are close to the limit. Only the heterostructures conductivity can be fairly different. From the linear used for group C devices (d ~ 0.04 µm, L ~ 0.8 µm) can approximation of the carrier density versus gate depen- be used for fabricating shorter gate length transistors.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 MAGNETOTRANSPORT CHARACTERIZATION OF THz DETECTORS 145

The minimum gate length for these transistors is 4. P. J. Burke, R. J. Schoelkopf, D. E. Prober, et al., J. Appl. approximately 0.2 µm. One can expect then to reach a Phys. 85, 1644 (1999). maximum detection frequency of about 2.4 THz with a 5. B. S. Karasik, W. R. McGrath, M. E. Gershenson, and maximal quality factor of about 6. A. V. Sergeev, J. Appl. Phys. 87, 7586 (2000). In conclusion, transistors processed from 6. T. W. Crow, R. J. Mattauch, R. M. Weikle, and GaAs/GaAlAs and GaInAs/GaAlAs heterostructures U. V. Bhapkar, in Compound Semiconductor Electron- were investigated by magnetotransport measurements ics, Ed. by M. Shur (World Sci., Singapore, 1996), p. in order to characterize their applicability as resonant 209. tunable detectors of THz radiation. We showed how the 7. S. M. Marazita, W. L. Bishop, J. L. Hesler, et al., IEEE electron mobility in the transistor can be evaluated Trans. Electron Devices 47, 1152 (2000). from a magnetic-ﬁeld dependence of the transistor 8. E. E. Haller and J. W. Beeman, in Proceedings of Far-IR, resistance. High-mobility GaAs/GaAlAs transistors Submm and mm Detector Technology Workshop, with a quality factor approaching 10 were fabricated. Monterey, CA (2002) (in press). These devices are the most promising (among those 9. G. E. Stillman, C. M. Wolfe, and J. O. Dimmock, Solid investigated) devices for application as resonant detec- State Commun. 7, 5 (1969). tors. 10. W. Knap, J. Lusakowski, K. Karpierz, et al., J. Appl. Phys. 72, 680 (1992). 11. For review see M. Dyakonov and M. S. Shur, in Tera- ACKNOWLEDGMENTS hertz Sources and Systems, Ed. by R. E. Miles, P. Harri- We thank M. Dyakonov and S. Rumyantsev for son, and D. Lippens (Kluwer Academic, Dordrecht, helpful discussions. 2001), p. 187. Financial support from NATO linkage grant 12. M. Dyakonov and M. S. Shur, Phys. Rev. Lett. 71, 2465 no. CLG977520 “Semiconductor Sources for Terahertz (1993); IEEE Trans. Electron Devices 43, 380 (1996); in Proceedings of 22nd International Symposium on GaAs Generation” is highly acknowledged. The work at RPI and Related Compounds (1996), Inst. Conf. Ser., was supported by the National Science Foundation No. 145, Chap. 5, p. 785. (Program Monitor Dr. James Mink). 13. W. Knap, Y. Deng, S. Rumyantsev, et al., Appl. Phys. Lett. 80, 3433 (2002). REFERENCES 14. W. Knap, Y. Deng, S. Rumyantsev, and M. S. Shur, Appl. 1. A. C. Samuels, D. L. Woolard, T. Globus, et al., in Phys. Lett. 81, 4637 (2002). WOFE-02 Proceedings, Yoon Soo Park, Ed. by 15. X. G. Peralta, S. J. Allen, M. C. Wanke, et al., Appl. M. S. Shur and William Tang (2002). Phys. Lett. 81, 1627 (2002). 2. B. Ferguson and X.-C. Zhang, Nature Mater. 1, 26 16. W. Knap, V. Kachorovskii, Y. Deng, et al., J. Appl. Phys. (2002). 91, 9346 (2002). 3. M. Kroug, S. Cherednichenko, H. Merkel, et al., IEEE 17. A. A. Grinberg and M. S. Shur, J. Appl. Phys. 58, 382 Trans. Appl. Supercond. 11, 962 (2001). (1985).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 146Ð149. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 146Ð149. Original Russian Text Copyright © 2004 by Antonov, Gavrilenko, Demidov, Morozov, Dubinov, Lusakowski, Knap, Dyakonova, Kaminska, Piotrowska, Golaszewska, Shur.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Electron Transport and Terahertz Radiation Detection in Submicrometer-Sized GaAs/AlGaAs Field-Effect Transistors with Two-Dimensional Electron Gas A. V. Antonov1, V. I. Gavrilenko1, E. V. Demidov1, S. V. Morozov1, A. A. Dubinov1, J. Lusakowski2, 3, W. Knap2, 5, N. Dyakonova2, E. Kaminska4, A. Piotrowska4, K. Golaszewska4, and M. S. Shur5 1 Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected] 2 GES–UMR, CNRS–Université Montpellier 2, Montpellier, 34950 France 3 Institute of Experimental Physics, University of Warsaw, Warsaw, 00-681 Poland 4 Institute of Electron Technology, Warsaw, 02-668 Poland 5 Rensselaer Polytechnic Institute, Troy, N.Y., 121180-3590 USA

Abstract—The electronic transport and response in the terahertz range are studied in ﬁeld-effect GaAs/AlGaAs transistors with a two-dimensional high-mobility electron gas. The special interest expressed in such transistors stems from the possibility of developing terahertz-range radiation detectors and generators on the basis of these devices. Measurements of the value and the magnetic-ﬁeld dependence of the drain–source resistance are used to estimate the electron density and mobility in the transistor channel. Results of magnetotransport measurements are employed to interpret the nonresonant detection observed in transistors with a gate width from 0.8 to 2.5 µm. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION detector. A field-effect transistor with a 2D electron gas in the channel can be used as such a detector. Under Recently, great interest has been shown in terahertz- ordinary operating conditions, the upper limiting fre- range radiation detection by means of semiconductor quency of the field-effect transistor is dictated by the devices based on plasma effects. Resonant and nonresonant detection in field-effect transistors with a two- inverse electron transit time through the region under dimensional (2D) electron gas was observed in [1Ð4]. the gate. The use of plasma effects makes it possible to Those studies were aimed at the development of fast increase the operating frequency of submicrometer voltage-controlled terahertz-radiation detectors. The field-effect transistors up to the terahertz frequency terahertz range (0.3Ð10 THz) corresponds to frequen- range [12], since the characteristic velocities of plasma cies of many excitations in condensed media, such as waves can be as high as 108 cm sÐ1, which is signifi- phonons, transitions with the participation of shallow cantly higher than the electron drift velocity in the tran- impurities, cyclotron and paramagnetic resonances, sistor channel. Resonant detection of terahertz radia- and rotational and vibrational excitations in liquids, tion has already been demonstrated for two types of gases, and biological objects. Main interest is in the use field-effect transistors, namely, for a commercial field- of terahertz radiation in nondestructive testing, visual- effect GaAs/AlGaAs transistor [1,2] and a field-effect ization, medicine, environmental monitoring, the food transistor with a double quantum well and a grating industry, and the struggle against terrorism [5, 6]. Cur- gate [3]. rently, broad-band detectors are mainly employed to detect terahertz radiation. The application of selective The resonant frequency of plasma oscillations in the and tunable detectors to spectral analysis makes it pos- 2D electron gas under the gate is determined by the gate sible to discard diffraction gratings or mechanically length L and the electron density n, which can be tunable interferometers. The sensitivity band can be approximately described by a simple formula for a tuned in semiconductor photoresistors (GaAs [7], InP plane capacitor, n = CU /e, where C is the gateÐchannel [8], InSb [9], GaAs/AlGaAs [10, 11]) placed in a mag- 0 netic field. However, such detectors always require capacitance per unit surface area, U0 = UGS Ð Uth is the cooling to liquid-helium temperature and magnetic gate-to-channel voltage swing (UGS is the voltage fields of several teslas. In many cases, it is preferable to applied to the gate, Uth is the pinch-off voltage of the operate with a voltage-tunable terahertz-radiation transistor), and e is the elementary charge. In the case

ELECTRON TRANSPORT AND TERAHERTZ RADIATION DETECTION 147

6 6 A A –5 –5 4 4 , 10 , 10 SD SD I I 2 2

0 –0.4 –0.3 –0.2 –0.1 0 00.2 0.4 0.6 0.8 1.0 , T UGS, V B

Fig. 1. Transfer characteristics of transistor T3* measured at Fig. 2. Magnetic-ﬁeld dependences of the source–drain cur- magnetic ﬁelds varied from 0 (upper curve) to 0.4 T with a rent of transistor T3* for gate voltage UGS varied from 0 step of 0.05 T and from 0.4 to 1 T with a step of 0.1 T. The (upper curve) to Ð0.4 V (with a step of 0.01 V) constructed sourceÐdrain voltage is 20 mV. on the basis of the curves in Fig. 1.

of large values of U0, the resonant frequency is given by sistors. Measurements were carried out at a fixed radi- the simple expression ation frequency and amplitude modulation at a frequency of 200Ð1000 Hz. The photovoltage in the 1 eU0 sourceÐdrain circuit was measured at a negative dc volt- f 0 = ------. (1) 4L m age UGS applied to the gate with respect to the source. A conventional lock-in amplifier circuit was used. The The resonant frequency is highest for a zero gate volt- signal from the lock-in amplifier output and the gate age and vanishes as UGS approaches the pinch-off voltage were stored on a computer by using an analog- voltage. to-digital converter. To determine the transistor parameters, the channel dc conductance was measured as a 2. EXPERIMENTAL function of the gate voltage and the normal magnetic field. The transistors under study were produced from a GaAs/AlGaAs heterostructure with a 2D high-mobility electron gas, grown through molecular-beam epitaxy. The distance from the surface to the conducting channel was approximately 160 nm and the drainÐsource 7 distance was 10 µm for all the transistors. In this paper, 2.0 4 we present the measurement results for two transistors with a gate length of 0.8 µm (T2) and 2.5 µm (T3, T3*) –3 µ µ 1.5 5 and a channel width of 50 m (T2, T3*) and 100 m ×10

(T3). The gate was positioned in the immediate vicinity S of the source. The crystal with the transistors was 1.0 mounted on a holder for integrated circuits, which then 2 3 was placed into a countermodule positioned in a light- guide insert in an STG-40 transport helium Dewar. All 0.5 measurements were carried out at T = 4.2 K. Bonding 1 Photoresponse, arb. units 1 Counductance, pads of the transistors were connected with holder pins 0 3 by gold wires. The same pads, together with lead-in 0 metal strips, played the role of a receiving antenna for –1.5–1.0 –0.5 0 terahertz radiation. As radiation sources in the range f = UGS, V 50Ð700 GHz, we used backward-wave tubes (BWTs) OV-74, OV-32, and OV-30, as well as BWT-based G4- 161 and G4-142 signal generators. Radiation was intro- Fig. 3. Gate-voltage dependences of the transistor T2 photoresponse (1, 2) measured by us and (3) calculated using duced into the transport helium Dewar via a light guide formula (22) from [4] and (4) the measured transfer charac- (polished stainless-steel tube) and was focused with the teristic of the transistor for different values of f: (1, 3) 329 use of a polished brass cone onto the crystal with tran- and (2) 228 GHz.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

148 ANTONOV et al.

1.25 5 10 1.0 12 3456 –3 8 10 ×

S 0.75 6 0.5 2 4 1 Conductance,

3 Photoresponse, arb. units Photoresponse, arb. units 0.25 2 0 4 0 0 –0.50 –0.25 0 –1.0–0.6 –0.2 0 UGS, V UGS, V

Fig. 4. (1Ð4) Gate-voltage dependences of the transistor T3 Fig. 5. Gate-voltage dependences of the transistor T3 pho- photoresponse and (5) the transfer characteristic of the tran- toresponse (1) for the highest radiation power and (2Ð6) for sistor for different values of f: (1) 597, (2) 629, (3) 655, and a sequential decrease in the power by half. All the curves are (4) 682 GHz. normalized to the strongest response; f = 78 GHz.

3. RESULTS AND DISCUSSION sponse is nonresonant in nature. Rough estimation of the detector sensitivity yields 103 V/W. We can see from Figure 1 shows the typical gate-voltage depen- Fig. 3 that the dependence of the signal on the gate volt- dences of the transistor sourceÐdrain current I at var- SD age conforms well to that calculated within the nonres- ious magnetic fields. In Fig. 2, these data are recon- onant-response model [4]. Qualitatively, the signal fal- structed as magnetic-field dependences at a fixed gate loff in the range of high gate voltages can be explained voltage. It can be seen that the transistor is off at the by total depletion of the channel. The falloff observed pinch-off voltage Uth = Ð(0.35Ð0.40) V. By using the as UGS decreases can be associated with the increase in dependence of the current on the magnetic field, we can the channel conductance and with the worse deviceÐ estimate the carrier mobility in the channel from the µ antenna matching. formula B1/2 = 1, where B1/2 is the magnetic field at which the current decreases by half. For the data shown Figure 4 shows the gate-voltage dependences of the in Fig. 2, this estimation yields µ ≈ 7.5 × 104 cm2/V s at photoresponse for transistor T3 with an atypical trans- U = 0. With this estimate, the lower frequency limit fer characteristic (curve 5). This transistor had a chan- GS µ for the observation of a resonant response can be found nel split into two equal regions each 50 m wide. We from the condition ωτ = 1 to be 50 GHz. can readily see that the transfer characteristic has two portions corresponding to two values of the pinch-off Figure 3 shows the typical gate-voltage depen- voltage (approximately Ð0.2 and Ð0.4 V). Each of these dences of the transistor photoresponse, as well as the pinch-off voltage values is associated with a feature measured transfer characteristic. The observed pinch- observed in the nonresonant response as a function of off voltage Uth = Ð0.3 V at a zero gate voltage corre- the gate voltage. sponds, according to Eq. (1), to the resonance fre- Figure 5 illustrates the operation of the transistor as quency f(0) = 270 GHz, which should vanish as UGS increases from zero to Ð0.3 V. Thus, the frequency of a microwave detector in the nonlinear mode. It is easily 329 GHz (curve 1 in Fig. 3) exceeds the highest reso- seen that the gate-voltage dependence of the photore- nant frequency. On the contrary, the frequency of sponse is “pulled” into the region of higher negative 228 GHz (curve 2) is lower than f(0) and, according to UGS as the radiation power increases, which seems to be Eq. (1), becomes equal to the plasma frequency of the caused by a commensurate increase in the amplitude of ≈ the high-frequency gate voltage. electron gas under the gate at UGS Ð0.1 V. However, it can be seen that, in this range of the gate voltages, curve 2 in Fig. 3 exhibits no features that could be associated with the resonant response.1 The observed photore- REFERENCES

1 1. W. Knap, Y. Deng, S. Rumyantsev, et al., Appl. Phys. It is the authors' opinion that the absence of a resonant response Lett. 80 (18), 3433 (2002). (in contrast to the data from [1, 2]) can be caused by an insufﬁ- ciently strong connection of the “plasma resonator” with other 2. W. Knap, Y. Deng, S. Rumyantsev, and M. S. Shur, Appl. elements of the equivalent electric circuit of the transistor. As a Phys. Lett. 81 (24), 4637 (2002). result, the resonant response (which should be observed as UGS increases from zero to the pinch-off voltage) can be concealed by 3. X. G. Peralta, S. J. Allen, M. C. Wanker, et al., Appl. the increasing nonresonant response. Phys. Lett. 81 (9), 1627 (2002).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 ELECTRON TRANSPORT AND TERAHERTZ RADIATION DETECTION 149

4. W. Knap, V. Kachorovskii, Y. Deng, et al., J. Appl. Phys. 8. W. Knap, J. Lusakowskii, K. Karpierz, et al., J. Appl. 91 (11), 9346 (2002). Phys. 72 (2), 680 (1992). 9. G. Strasser, K. Bochter, M. Witzany, and E. Gornik, 5. A. C. Samuels, D. L. Woolard, T. Globus, et al., in Envi- Infrared Phys. 32, 439 (1991). ronmental Sensing of Chemical and Biological Warfare 10. Y. Kawano, Y. Hisanaga, H. Takenouchi, and S. Ko- Agents in the THz Region, WOFE-0.2 Proceedings, Yoon miyama, J. Appl. Phys. 89 (7), 4037 (2001). Soo Park, Ed. by Michael S. Shur and William Tang (2002). 11. B. A. Andreev, I. V. Erofeeva, V. I. Gavrilenko, et al., Semicond. Sci. Technol. 16 (5), 300 (2001). 6. B. Ferguson and X.-C. Zhang, Nature Mater. 1 (1), 26 12. M. Dyakonov and M. S. Shur, Phys. Rev. Lett. 71 (15), (2002). 2465 (1993). 7. G. E. Stillman, C. M. Wolfe, and J. O. Dimmock, Solid State Commun. 7, 7 (1969). Translated by A. Kazantsev

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 150Ð152. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 150Ð151. Original Russian Text Copyright © 2004 by Veksler, Gavrilenko, Spirin.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Cyclotron Resonance of Holes in Silicon in Quantizing Magnetic Fields D. B. Veksler, V. I. Gavrilenko, and K. E. Spirin Institute of Microstructure Physics, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia

Abstract—The cyclotron resonance spectra of holes in bulk silicon in quantizing magnetic ﬁelds are investigated in the low-temperature range. The data obtained agree well with the results of the numerical calculation performed earlier by Owner-Petersen and Samuelsen for effective cyclotron masses m*/m0 and matrix elements M upon transitions between different Landau levels of holes in silicon with a magnetic-ﬁeld orientation H || [001]. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION frequency and T = 4.2 K. Samples of bulk silicon pre- × × It is well known that lower Landau levels of holes in pared in the form of plates 5 5 0.3 mm in size were diamond-like semiconductors of germanium and sili- placed in a fiber-optic waveguide insert into an STG-40 con are not equally spaced [1, 2]. This is a consequence of the degeneracy of the valence band at the point k = 0 and leads to the fact that, in strong magnetic fields 1 (a) បω ≥ ( c kBT), the cyclotron resonance spectra exhibit a large number of resonance lines associated with optical 0.297 transitions between different pairs of energy levels rather than two absorption lines attributed to light and 0.316 heavy holes. The cyclotron resonance of holes in quantizing magnetic fields has been thoroughly studied in germanium (see, for example, [3]). Surprising as it may 0.274 seem, only a few papers have been concerned with sim- 0.461 ilar investigations of the cyclotron resonance in silicon 0.154 0.220 [4, 5]. The most comprehensive data on the cyclotron 0.092 resonance spectra of holes in silicon in the limit of strong magnetic fields are presented in the paper by 0.250 Owner-Petersen and Samuelsen [5], who compared the 0 5 10 15 20 25 results of measurements performed for different orien- tations of the magnetic field with theoretical data. This 0.19(b) 0.42 comparison allowed those authors to refine considerably 1 the parameters of the dispersion law of holes in silicon

[5]. The above investigations were carried out using Adsorption, arb. units ρ Ω samples of high-resistance p-Si ( 300 K = 3.9 k cm) in the millimeter-wave band ( j = 45 GHz) at temperatures ranging from 1.2 to 5 K. In this work, we carried out similar investigations 0.30 ρ ≈ Ω using a purer sample of n-Si ( 300 K 10 k cm) in the short-wavelength part of the millimeter-wave band at 0.15 T = 4.2 K. A comparison of our results with the theoretical data obtained earlier in [5] showed that the parameters of the dispersion law of holes in silicon call for further reﬁnement. 0 5 10 15 H, kOe

2. SAMPLES AND EXPERIMENTAL TECHNIQUE Fig. 1. Cyclotron resonance spectra of photocarriers in silicon at a temperature of 4.2 K and frequencies of (a) 142.8 The cyclotron resonance spectra were measured in and (b) 75 GHz. Numbers at the peaks of the curves are the the automatic magnetic-ﬁeld scan mode at a constant cyclotron masses (expressed in units of m0).

CYCLOTRON RESONANCE OF HOLES IN SILICON 151 helium storage dewar situated at the center of a super- 20 conducting solenoid in such a manner that the magnetic H || [001] ﬁeld was directed perpendicular to the plane of the sample: H || [001]. Generators based on G4-161 and G4- ε ε 142 backward-wave tubes were used as radiation 1 levels 2 levels sources in the two- and four-millimeter-wave bands, respectively. Free carriers in samples were created c

0 (4, 2) under exposure to band-to-band radiation modulated at (4, 2) m a frequency of 1 kHz with the use of a gallium arsenide / (4, 1) (4, 1) light-emitting diode (λ ≈ 0.9 µm) located near the sam- eH ប 10 (3, 2) ple. The microwave radiation passed through the sam- (3, 2) ple was detected using an n-InSb crystal. The synchro- (3, 1) nous detection of signals was accomplished by a stan- (3, 1) dard method, after which the signals were digitized and Energy, (2, 2) (2, 2) entered on a personal computer with the use of an ana- (2, 1) log-to-digital converter. (2, 1) (1, 2) (1, 2) 3. RESULTS AND DISCUSSION (1, 1) (1, 1) 0 The experimental cyclotron resonance spectra are shown in Fig. 1. In addition to the lines attributed to cyclotron resonances of electrons (m*/m = 0.19 and Fig. 2. Calculated energy diagram of lower Landau levels of 0 holes in silicon for the following set of band parameters: γ γ γ κ 0.42), the spectra exhibit a large number of resonances 1 = 4.25, 2 = 0.35, 3 = 1.39, and = Ð0.46 [5]. due to transitions between different Landau levels of holes that are not equally spaced. The transitions characterized by cyclotron masses of approximately 0.15m 0 Transition 9 is characterized by an effective cyclotron and 0.5m correspond to cyclotron resonances of the 0 mass of 0.292m . As a rough approximation, this tran- classical light and heavy holes, respectively, i.e., cyclo- 0 tron resonances of the holes occupying Landau levels sition corresponds to the cyclotron resonance line with large indices. At the same time, the hole lines observed at an effective cyclotron mass of 0.297m0 in located between the lines associated with cyclotron res- the spectrum shown in Fig. 1a. Another pronounced onances of electrons are attributed to transitions line of the quantum cyclotron resonance of holes, between lower Landau levels that are not equally which is observed at an effective cyclotron mass of spaced. It is evident that, in strong (quantizing) mag- បω netic fields [i.e., in the case when the ratios /kBT are sufficiently large (Fig. 1a)], the relative intensities of Calculated values of the effective cyclotron masses m*/m0 “quantum” cyclotron resonance lines (corresponding to and matrix elements M for transitions between different Lan- effective cyclotron masses of approximately 0.3m0) are dau levels of holes in silicon with magnetic-field orientation considerably higher than those in Fig. 1b. The resolu- H || [001] [5] tion of the lines associated with the quantum cyclotron resonance of holes in the spectrum recorded in this No. m*/m0 M Transition work (Fig. 1a) is substantially higher than that in the ε 1 0.224 0.495 1(2, 1) (3, 2) spectrum obtained in [5], even though, in the latter ε បω 2 0.232 0.432 1(1, 1) (2, 2) case, the ratio /kBT is somewhat greater. The better ε resolution of the cyclotron resonance lines of holes in 3 0.264 1.061 2(1, 2) (2, 2) ε our spectrum can be explained by the higher purity of 4 0.270 1.80 1(3, 2) (4, 2) the sample. ε 5 0.273 1.46 1(2, 2) (3, 2) Figure 2 presents the energy diagram of the lower 6 0.285 1.07 ε (1, 1) (2, 1) Landau levels of holes according to the calculations 1 ε performed in [5]. The table lists the effective cyclotron 7 0.286 1.56 2(2, 2) (3, 2) ε masses and matrix elements for the energy-level transi- 8 0.287 1.70 2(3, 1) (4, 1) tions. Transitions 3Ð13 each occur within their own lad- 9 0.292 1.04 ε (1, 2) (2, 2) der of Landau levels and have comparable values of the 1 បω ≥ 10 0.305 1.52 ε (2, 1) (3, 1) matrix elements. In strong magnetic fields ( /kBT 1 ε 1), the cyclotron resonance spectra should predomi- 11 0.314 1.45 2(2, 1) (3, 1) nantly contain lines attributed to transitions from the ε 12 0.314 1.85 1(3, 1) (4, 1) lower Landau levels of holes. Three of the four transi- ε tions (transitions 3, 6, 9) are presented in the table. 13 0.319 1.99 2(3, 2) (4, 2)

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

152 VEKSLER et al.

0.316m0 in the spectrum depicted in Fig. 1a, can be ACKNOWLEDGMENTS assigned to transitions 11Ð13 (see table). However, all This work was supported by the Russian Foundation these transitions occur not from the lower but from the for Basic Research (project no. 03-02-16808) and the higher Landau levels; consequently, their intensities Ministry of Industry, Science, and Technology of the Rus- should not be very high. The last (fourth) transition sian Federation (State Contract no. 40.072.1.1.1173). from one of the four lower Landau levels, namely, ε (1, 1) (2, 1) (not included in the table), is charac- 2 REFERENCES terized by an effective cyclotron mass of 0.32m0. There- fore, it is reasonable to assume that this transition cor- 1. J. M. Luttiger and W. Kohn, Phys. Rev. 97 (4), 869 responds to the cyclotron resonance line observed at an (1955). 2. J. M. Luttiger, Phys. Rev. 102 (4), 1030 (1956). effective mass of 0.316m0 in our spectrum (Fig. 1a). In order to obtain the ultimate answer to this problem, it is 3. J. C. Hensel and K. Suzuki, Phys. Rev. B 9 (10), 4184 necessary to measure the cyclotron resonance in stron- (1974); Phys. Rev. B 9 (10), 4219 (1974). ger magnetic fields (at the same temperature). As was 4. J. J. Stickler, H. J. Zeiger, and G. H. Heller, Phys. Rev. noted in [5], it is at this orientation of the magnetic field 127 (4), 1077 (1962). H || [001] that the energy location of the transitions 5. M. Owner-Petersen and M. R. Samuelsen, Phys. Status from the four lower Landau levels is most sensitive to Solidi 28, 211 (1968). γ the parameter 2 of the dispersion law of holes, which can thus be refined. Translated by O. Moskalev

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 153Ð156. From Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 152Ð155. Original English Text Copyright © 2004 by Popov, Teperik, Polischuk, Peralta, Allen, Horing, Wanke.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Plasmon-Induced Terahertz Absorption and Photoconductivity in a Grid-Gated Double-Quantum-Well Structure* V. V. Popov1, T. V. Teperik1, O. V. Polischuk1, X. G. Peralta2, S. J. Allen2, N. J. M. Horing3, and M. C. Wanke4 1 Institute of Radio Engineering and Electronics, Saratov Division, Russian Academy of Sciences, Saratov, 410019 Russia 2 Center for Terahertz Science and Technology, University of California, Santa Barbara, California, 93106 USA 3 Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, New Jersey, 07030 USA 4 Sandia National Laboratories, Albuquerque, New Mexico, 87185 USA

Abstract—The terahertz absorption spectra of plasmon modes in a grid-gated double-quantum-well ﬁeld- effect transistor structure is analyzed theoretically and numerically using the scattering matrix approach and is shown to faithfully reproduce strong resonant features of recent experimental observations of terahertz photoconductivity in such a structure. © 2004 MAIK “Nauka/Interperiodica”.

* Recently, the terahertz (THz) photoconductivity of a Far infrared absorption in density-modulated two- double-quantum-well (DQW) ﬁeld-effect transistor dimensional electron systems has been studied theoret- (FET) with a periodic metal-grid gate was observed [1]. ically in a series of papers [2Ð9], including studies of It appears that the presence of a DQW is important to density-modulated bilayers [2, 4, 6] and structures with produce a strong photoresponse. The position and the metal gratings [3, 5]. strength of the peaks in the photoresponse and photo- In this paper, we develop a detailed, realistic model conductance (the change of channel conductance) are of plasmon electrodynamics in the grid-gated DQW controlled by both the voltage Vg applied to the gate and FET structure studied experimentally in [1]. We present the period of the grating gate, which strongly suggests the results of our electrodynamic simulation of the THz that the sharp resonant features are related to plasma absorption spectrum taking into account all essential oscillations in this composite device. The strongest features of the actual composite structure studied in [1], THz photoresponse occurs when the upper QW is fully which faithfully reproduce strong resonant features of depleted under metallic portions of the grating gate, experimental observations of THz photoconductivity in while the lower one remains connected but with later- such a structure. ally modulated electron density. The response is fast (less than 1 µs) and depends on the presence of the DQW channel. Remarkably, the sharpest and strongest 1. THEORETICAL MODEL resonance response does not occur at the lowest tem- We analyze the THz absorption spectrum in the peratures but rather between 25 and 40 K. The sign of DQW multilayered laterally periodic structure from [1] the photoconductance is not unique and depends on the (see inset to Fig. 1a) using a scattering matrix approach grating period. The physical mechanism responsible [10Ð12]. The scattering matrix approach employed for the THz photoconductivity is not evident at this involves the following steps. Within each layer of the time. Particularly, the temperature dependence, as well structure, the Maxwell equations are rewritten in an inas the reversal of sign of the photoconductance, is not plane momentum matrix representation starting with understood. decomposition of the magnetic ﬁeld into a sum of plane A simple “transmission” model discussed in [1] waves: describing plasma oscillations in the grid-gated DQW (),, FET provided a rough qualitative guide suggesting that H xzt the series of frequency-dependent resonances observed (1) ()β ()()ω in the THz photoconductance corresponds to the exci- = ∑Hm exp Ði m x exp ikzz exp Ði t , tation of plasma waves in the structure. However, this m simple model fails to explain the measured separation where m = 0, ±1, ±2, …, ±M; β = k + 2πm/L; L is the in Vg between resonances at different frequencies and m x the variation of the line shape with frequency. period of the structure; and kx is the reduced in-plane wave vector. In the case under consideration, when THz *This article was submitted by the authors in English. radiation is incident normally onto the multilayered

154 POPOV et al.

0.08 (a) 0.03 (b) 570 GHz z 4 µm period L Metal grid 0.06 w 0.02 x DQW 0.04 600 Absorbance 630 Absorbance 0.01 µ 0.02 660 8 m period

0 0

0.15 0.06 (c) (d) 570 GHz 0.10 4 µm period 0.04

0.05 0.02 600

630 0

660 Photoresponse, arb. units Photoresponse, arb. units 0 8 µm period –0.05 –2.0 –1.5 –1.0 –0.5 0 –2.5 –2.0 –1.5 –1.0 –0.5 0 Vg, V Vg, V

Fig. 1. Calculated absorption spectra: (a) at several different THz frequencies for L = 4 µm and w = L/2 and (b) at a frequency of 600 GHz for two different periods of the structure with w = L/2; Vth = Ð2.6 V is a ﬁtted value. Other parameters of the structure are given in the text. Terahertz photoresponse measured as a function of gate voltage: (c) for four different frequencies for L = 4 µm and w = L/2 and (d) at a frequency of 600 GHz for different periods of the metal gate with w = L/2 at T = 25 K, as reported in [1].

structure, kx = 0 and there are only Ex0 and Hy0 nonzero where n = 1, 2, …, 2M + 1, have normalized amplitudes components of the electric and magnetic field in the of the magnetic field Hym as their components. Eigen- incident wave. Assuming the square profile of the lat- vectors A(n) and A(n') corresponding to eigenvalues eral periodicity of the structure, the dielectric function () () n 2 n' 2 ε(x) in each layer transforms into matrix εˆ with ele- ()kz and (kz ) satisfy the orthogonality relationship (n) (n') δ ments A A = nn'. In particular, for homogeneous layers, (n) L/2 the eigenvalue problem (3) yields the eigenvectors A 2π()mmÐ ' with components δ corresponding to eigenvalues ε = ε()x exp Ð------dx. (2) nm mm' ∫ L ÐL/2 ω2 ()()n 2 ε δ β kz = ------Ð nm m. Obviously, for homogeneous layers, we have εˆ = εÎ , c2 where ε is constant and Î is the unit matrix. Eigenproblem (3) is degenerate with respect to the As a result, in each layer, we arrive at the matrix reversal of sign of the transverse wave vector k . Thus, eigenproblem z the total field in each layer is a superposition of eigen- 2 ()n ω Ð1 2 ± εˆ βˆ εˆ βˆ modes of form (1) with kz = kz , where n = 1, 2, …, -----2- Ð A = kz A, (3) c 2M + 1, propagating along and counter to z axis. Apply- ing boundary conditions of continuity of Ex and Hy βˆ β where is the diagonal matrix with elements mm' = components of the total field at interfaces of the layers, δ β (n) mm' m. The (2M + 1)-dimensional eigenvectors A , we can relate the amplitudes of waves outgoing from

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 PLASMON-INDUCED TERAHERTZ ABSORPTION AND PHOTOCONDUCTIVITY 155 the whole structure to those of incoming waves in the The electron density in the lower QW under metallic matrix form: portions of the grating gate as a function of the gate

+ + voltage NL(Vg) was obtained from the parallel plate Aout Ain capacitor model with the gate voltage depletion thresh- = ޓ. Ð Ð old value Vth and zero-gate-voltage electron density in Aout Ain both QWs combined chosen as fitting parameters to the Here, superscripts + and Ð refer to the waves propagat- experimental data of [1]. The parallel plate capacitor ing along and counter to the z axis, respectively, and model assumed in this paper is fairly well justified for ޓ characteristic parameters of the structure studied in [1]: is the scattering matrix of the whole structure, which ӷ ∆ can be written in the 2 × 2 block matrix form: L h > d, . This electrostatics problem is solved separately, and the obtained value NL(Vg) is used as an input parameter in electrodynamic modeling. The metal ˆ ˆ ޓ = S11 S12 . grating strips are composed of a 20-nm Ti layer covered  by a 50-nm Au layer. We took the bulk conductivities as Sˆ 21 Sˆ 22 σ × 4 σ × 5 0 = 2.3 10 S/cm for Ti and 0 = 4.85 10 S/cm In our particular problem under consideration, we have for Au. only one incoming plane wave incident onto the metal- Dielectric function ε(x) entering expression (2) in + grid gate (i.e., Ain = 0) and there is only the m = 0 non- QW layers is taken as Ð πσ () zero component in the vector Ain . Thus, we can calcu- 4 UL()x ε ()()x = ε+ i------, late the amplitudes of reflected and transmitted waves UL b ω as ε where b = 12.24 in the background dielectric constant. + ˆ Ð Ð ˆ Ð ε πσ ω Aout ==S12Ain , Aout S22Ain . Inside the metal-grid layer, we assume (x) = i4 0/ at the metal strips and ε(x) ≡ 0 at the grid openings. Since the period of the structure under consideration (L Ӎ 4 µm) is roughly two orders of magnitude shorter than the THz radiation wavelength, only m = 0 plane- 2. RESULTS AND DISCUSSION wave components in the reflected and transmitted Figure 1a shows the resonant absorption of incident waves survive at distances much longer than L away ≠ THz electromagnetic radiation at several frequencies from the structure, while all m 0 plane-wave compo- versus gate voltage. It is seen in Figs. 1a and 1c that the nents are evanescent. Ultimately, we can readily calcu- variation in the line shape of plasma resonances with late reflectivity R, transmittivity T, and absorbance A = frequency is very close to that observed in photocon- 1 Ð R Ð T. For more detailed description of the scattering ductivity resonances. In our calculations, we used a fit- matrix formalism for multilayered laterally periodic τ Ð11 structures, see, for example, [12]. ting parameter = 10 s. This is roughly an order of magnitude less than the value extracted from the DC In carrying out our calculations, we assume that the mobility [1]. Although the THz measurement tempera- effective thickness d of the upper and lower QWs in the tures are substantially above that used to measure the DQW structure is 10 nm each, the separation between ∆ DC mobility, it is not likely that the DV mobility has the center planes of the QWs = 27 nm, and the dis- dropped by an order of magnitude. On the other hand, tance between the upper (near to the metal-grid gate) one may consider an inhomogeneous broadening of the QW and grating gate h = 385 nm. We assume that the plasma resonance: the mean free time for a carrier to upper QW is fully depleted under the metallic portions traverse a period of the modulation is ~L/vF, where vF of the grating gate of period L, forming an array of dis- is the Fermi velocity of electrons in the QWs, yielding connected electron strips of width w with surface elec- Ð11 × 11 Ð2 ~10 s for characteristic parameters of the structure tron density NU = 1.7 10 cm . The lower QW is under consideration, which is the same order of magni- × 11 Ð2 density modulated with NL = 2.57 10 cm , which tude as the scattering used to fit the data. remains essentially unchanged under the electron strips The calculated THz absorption spectra and mea- of the upper QW (i.e., under the open parts of the grat- sured THz photoresponse for two different periods of ing gate). The response of electron gas in QWs to the ω the DQW FET structure are shown in Figs. 1b and 1d. terahertz electric field Eexp(Ði t) is described by a It is evident, for both periods, that the positions of the local bulk conductivity in the Drude form, resonances in photoresponse relate to those of the cor- 2 () τ responding plasma resonances, although the signs of σ () e NUL()x UL()x = ------, the photoresponse measurements are opposite for the m*d 1 Ð iωτ different periods involved. where e and m* are the electron charge and effective It can be seen in Fig. 1 that the separation between mass and τ is the phenomenological electron relaxation the resonances of THz photoresponse exceeds the cal- time. culated separation by about 15%. This may be due to

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 156 POPOV et al. the fact that the parallel plate capacitor model we use to Martin Company, for the United States Department of calculate the equilibrium electron density in the lower Energy’s National Nuclear Security Administration QW suffers from a neglect of fringing ﬁeld effects. under contract no. DE-AC04-94AL85000. N.J.M.H. While the resonant positions and strengths are well gratefully acknowledges support from the US Depart- reproduced by our electrodynamic model, it has not ment of Defense, DAAD 19-01-1-0592. T.V.T. thanks dealt with the physical mechanism whereby excitation INTAS for its support (grant no. YSF 2002-153). of the plasmon resonances induces changes in the DC transport. The sign change shown in Fig. 1d under- REFERENCES scores the fact that this mechanism is not at all understood. 1. X. G. Peralta, S. J. Allen, M. C. Wanke, et al., Appl. More sophisticated modeling taking into account Phys. Lett. 81, 1627 (2002). the interwell electron transfer in grid-gated DQW FET 2. S. Katayama, J. Phys. Soc. Jpn. 60, 1123 (1991). structures is now in progress. We believe that this will 3. R. J. Wilkinson, C. D. Ager, T. Dufﬁeld, et al., J. Appl. provide an even better correspondence between theo- Phys. 71, 6049 (1992). retical and experimental results, as well as advance 4. S. Katayama, Surf. Sci. 263, 359 (1992). understanding of the physical mechanism that gives 5. L. Schaich, P. W. Park, and A. H. MacDonald, Phys. Rev. rise to the change in conductance at resonance. B 46, 12643 (1992). 6. C. Steinebach, D. Heitmann, and V. Gudmundsson, Phys. Rev. B 56, 6742 (1997). ACKNOWLEDGMENTS 7. B. P. Van Zyl and E. Zaremba, Phys. Rev. B 59, 2079 At the Institute of Radio Engineering and Electron- (1999). ics (Saratov Division), this work was supported by the 8. O. R. Matov, O. F. Meshkov, and V. V. Popov, Zh. Éksp. Russian Foundation for Basic Research (grant no. 03- Teor. Fiz. 113, 988 (1998) [JETP 86, 538 (1998)]. 02-17219). The work of X.G.P. and S.J.A. was sup- 9. O. R. Matov, O. V. Polischuk, and V. V. Popov, Zh. Éksp. ported by the ONR MFEL program, the DARPA/ONR Teor. Fiz. 122, 586 (2002) [JETP 95, 505 (2002)]. THz Technology, Sensing and Satellite Communica- 10. C. D. Ager and H. P. Hughes, Phys. Rev. B 44, 13452 tions Program, the ARO through Science and Technol- (1991). ogy of Nano/Molecular Electronics: Theory, Simula- 11. D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, tion, and Experimental Characterization, and the San- 2610 (1999). dia National Laboratory. Sandia is a multiprogram 12. S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, et al., laboratory operated by Sandia Corporation, a Lockheed Phys. Rev. B 66, 045102 (2002).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Destruction and Stabilization of the Electromagnetic Transparency of a Semiconductor Superlattice Yu. A. Romanov and Yu. Yu. Romanova Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected]

Abstract—Three types of transparency of a semiconductor superlattice, namely, self-induced, induced, and selective transparency, were studied. The conditions of their existence and the causes of their destruction were revealed. It was shown that the state of self-induced transparency, which is unstable in a harmonic ﬁeld, can be stable in a biharmonic ﬁeld. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION with a low electron concentration (the small parameter ω ω 2 ω Semiconductor superlattices (SLs) become strongly is ( 0/ 1) , where 0 is the plasma frequency charac- nonlinear and unstable media even in relatively weak terizing the linear oscillations of the SL plasma) and electric fields (102Ð104 V/cm) [1Ð4]. The nonlinearity only in transient processes or during a pulsed action on of high-frequency conductance manifests itself clearly the SL. as electromagnetic-transparency effects, such as self- In this work, we studied the mechanisms of destruc- induced transparency (SIT) [2, 3], induced transpar- 1 tion and stabilization of the SL electromagnetic trans- ency (IT) [4], and selective transparency (ST) [1]. The parency in a harmonic or biharmonic field, i.e., in a ST and SIT effects were predicted long ago, in the field of the type 1970s, and were observed experimentally in [5]. The mechanisms of their appearance were studied in [6, 7]. () ()ω δ ()ω δ Et = EC ++E1 cos 1t + 1 E2 cos 2t + 2 . (1) Electrons in SLs are known to exhibit Bloch oscillations (BOs) in a high-frequency field. Contrary to Bloch oscillations of an electron in a static electric 2. BASIC RELATIONS field, BOs in the general case are nonlinear and aperiodic [6]. Under the action of a harmonic field ω As is usually done, we use the sinusoidal electron E1cos( 1t), the dynamic localization (DL) of an elec- dispersion law tron occurs in SLs [8]; namely, the constant component of its velocity becomes zero at discrete values of the 2 2 បω ∆ ប k⊥ dimensionless field amplitude g1 = eE1d/ 1 corre- ε()k = --- ()1 Ð cos()k d + ------(2) sponding to the zeros of the zero-order Bessel function, 2 3 2m* J0(g1) = 0. In terms of quasi-energy, this effect corresponds to the collapse of electron quasi-energy mini- and the kinetic Boltzmann equation in the τ approxima- bands [9]. In the simplest case of constant relaxation tion time τ, SIT appears in the same fields [2, 3]. DL is (), () accompanied by the resonant excitation of electrons ∂f ()k, t eE() t ∂f ()k, t f k t Ð f 0 k caused by the harmonic field, and, hence, the absorp------∂ - + ------ប ------∂ - = Ð------τ , t k3 (3) tion of the field becomes maximal [6]. The absorbed (), () field energy can be transferred by electrons not only to f k 0 = f 0 k , the lattice but also to other fields to amplify them. This ប ប behavior can destroy both DL and SIT. Indeed, we where k3 and k⊥ are the longitudinal and transverse showed in [7] that SIT is unstable to both static and har- (with respect to the SL axis) components of the electron monic disturbances and can be observed only in an SL momentum បk, respectively; m* is the transverse effective electron mass; and f(k, t) and f0(k) are the field- 1 Note that, unlike optics, the electromagnetic transparency of an SL is thought to be the disappearance of the reactive component excited and equilibrium electron distribution functions, of a current [2, 3] rather than saturation of its dissipative compo- respectively. The electric field E is assumed to be uni- nent. form and directed along the SL axis.

158 ROMANOV, ROMANOVA

Using the periodicity of the electron distribution where the overscribed bar means time averaging. function in the k space, we represent this function in the form of a Fourier series, 3. SUPERLATTICE ∞ IN A BIHARMONIC FIELD f ()k, t = Fν()k⊥ exp()Φiνk d ν()t , ∑ 3 To study the interaction between fields in an SL, we ν∞= Ð (4) consider the behavior of the SL in biharmonic field (1) ω τ ӷ Ӷ Φ Φ with EC = 0, 1 1, g2 1, and arbitrary values of g1 ν = Ð*ν , ω Ω ω Ω ប and 2 (here, g1, 2 = 1, 2/ 1, 2, 1, 2 = eE1, 2d/ ). The where spectrum of BO velocity V(k0, t0, t) in this field consists π/d of three sets: the main spectrum [7], containing frequency ω and its harmonics () d () ()ν 1 Fν k⊥ = ------π ∫ f 0 k exp Ði k3d dk3, 2 Vk(),,t t = V sin[]k dg+ ()sin()ωt Ð sin()ωt Ðπ/d (5) 0 0 m 0 0 []()ψ() ()ψ, () (10) = V m cS k0t0 S t + ca k0 t0 a t Fν = FÐ*ν . [where k is the wave vector of an electron at the According to Eqs. (3)Ð(5), the multicomponent func- 0 instant t0, tion Φν satisfies the kinetic equation ψ () ()()ω S t = cos gsin t dΦν()t τ------+1,[]Φ1 + iντΩ()t ν()t = ∞ dt (6) = J ()g + 2 J ()g cos()2nωt , () 0 ∑ 2n Ω() edE t t = ------ប n = 1 ψ () ()()ω a t = sin gsin t with the initial conditions Φν(0) = 1. The electric cur- ∞ rent density is connected with Φ (t) by the relation 1 () ()()ω = 2∑ J2n Ð 1 g sin2n Ð 1 t , Φ end ∆ 〈ε 〉 〈ε 〉 j(t) = Ðj0Im( 1(t)), j0 = ------ប - ( /2 Ð 3 0), where 3 0 is n = 1 (), []()ω the mean equilibrium value of the longitudinal electron cS k0 t0 = sin k0dgÐ sin t0 , energy, d is the SL period, and n is the equilibrium elec- (), []()ω tron concentration in the SL. For an arbitrary time ca k0 t0 = cos k0dgÐ sin t0 , dependence of the field E(t) and for any electron disper- ∆ ប sion law, it is convenient to separate BOs by writing and V m = d/2 is the maximum longitudinal elec- Φ ±ω ν(t) in the form tron velocity in the SL] and two spectra shifted by 2: Φ () ()ψ() ∆ (),, ν t = aν t ν t , (7) Vk0 t0 t ∞ ψ ψ ν ν t Ω() where ν(t) = [ 1(t)] = exp(Ði ∫ t1 dt1 ) is the BO () [ ()ω δ 0 = V m ∑ Jn g1 cos k0dgÐ 1 sin 1t + 1 (11) eigenfunction, which is the solution to kinetic equation (6) n = Ð∞ without the collision integral and describes the dynamic ()]ω δ ()ω δ (collisionless) field-induced modulation of the electron + n 1t + 1 g2 sin 2t + 2 . distribution function. The dissipative function aν(t) ω ≠ ω At 2 n 1 (n is an integer), BOs are aperiodic and DL describes collision-induced changes in the electron distribution function and satisfies the equation [i.e., V (k0, t0) = 0] occurs at the same values of the field as in a purely harmonic field [i.e., at J0(g1) = 0] but only Ð1 Ð1 ∞ aúν()t + τ aν()t = τ ψν*()t . (8) for the averaging time t . In this case, according to Eqs. (7) and (8), the High-frequency BOs (whose spectrum contains only steady-state current at combination frequencies, which ω ω ӷ τÐ1 the frequencies = 0 and ) are slightly sup- is linear in the field E , is pressed by collisions. Averaging Eq. (8) over the time 2 interval ωÐ1 Ӷ ∆t Ӷ τ, we obtain ∞ 1 nn+ 0 ∆jt()= --- j g ∑ ()11+ ()Ð  2 0 2 () Φ() t ∞ aν t = ν 0 expÐτ-- n = Ð (9) ()()  Jn g1 Jn g1 t 1 ×  J ()g J ()g ------0 +1Ð exp Ð-- ψ*ν ()t + O ------, 0 1 nnÐ 0 1 2 τ ωτ  1 + ()γτ

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 DESTRUCTION AND STABILIZATION 159

J ()g J ()g (10) and (11) by only a modulating factor. At J0(g1) = 0, × []ω γ ) δ n0 1 n 1 γτ sin n 1 + t + n + ------2 the SL becomes transparent for both the field E1 (SIT) 1 + ()γτ τ and the field E2 (IT) in time ~ . ST appears immediately E after the application of the field and is determined by × cos()()nω + γ t + δ Ð -----2δ ()1 Ð δ (12) the condition of the absence of the corresponding har- 1 nn0 n00 E1 monics in BOs (10) and (11). Therefore, in the case of ω DL [J0(g1) = 0], only frequency 2 is absent in the non-  j g n steady-state current at t < τ, while the harmonics with ×ωcos()t + δ  Ð ------0 2()11+ ()Ð 0 ω ± ω 1 1 ω τ combination frequencies n 1 2 remain large. Note  1 that, beyond the τ = const approximation, the fields of () ω the disappearance of the total current and of only the An g1 2 ω × ------0 ()1 Ð δ + ------Bg()δ harmonic with frequency 2 are different. This impor- n00 ω 1 n00 n0 1 tant circumstance facilitates the separation of DL and collapse from IT in experimental studies. 1 |γ| Ӷ ω ×γcos()t + δ + O ------, (3) At 0 < 1, it is convenient to represent the 0 ω τ ω ω ± |γ| 1 BO spectra as consisting of triplets n 1, n 1 and a γ ω ω |γ| ω γτ doublet with ω = 0 and ω = |γ|. However, because of the where = 2 Ð n0 1; < 1; is arbitrary; n0 = 1, 2, … is the number of the strong-field harmonic whose system symmetry (odd-parity nonlinearity), a steady- state current contains only doublets and single lines at frequency is nearest to ω ; δ = (n Ð n )δ + δ ; δν is the 2 n 0 1 2 0 even n and only triplets at odd n . If |γ| ≤ τÐ1, the low- ∞ Ð2 2() 0 0 Kronecker delta; B(g) = ∑n = 1 n Jn g ; and frequency harmonic of BOs is heavily suppressed by collisions and the triplets are diffuse. This leads to sub- ∞ stantial changes in the amplitudes of all harmonics with () Ð1 () () Aν x = ∑ n Jn x Jn + ν x combination frequencies in the steady-state current. In n = Ð∞ this case, the averaged BO eigenfunction ν 2[]δ 2 Ð 1 n0 = --- ν0 Ð J0()x Jν Ð 1()x + ------Aν Ð 1()x Ð Aν Ð 2(),x ψν()t = J ()ννg Ð /2g J ()νg [()11Ð ()Ð x x 0 1 2 n0 1

n0 2 ×γ()δ ()γ() ()δ ] Ð1 ν cos t + 0 + i 11+ Ð sin t + 0 with A0 = 0 and A1(x) = x [1 Ð J0 (x)] ( = 1, 2, …). As ω τ Ð1 for the terms of the order ( 1 ) , we retained only the is not a constant (apart from the particular case when low-frequency term dominating over the other low-fre- J (νg ) = 0) and differs from zero at any value of g n0 1 1 quency terms in the ranges J (g ) ≅ 0 and J (g ) ≅ 0. ≠ 0 1 n0 1 and n0 0. Therefore, IT does not appear and the spec- We also retained one term quadratic in E2, which is nec- tra and character of ST of the current and BOs are dif- essary to understand the mechanism of resonance inter- ferent. action between the fields. These terms and the terms in (4) In addition to the absence of IT near the reso- γ ω ω which the amplitudes contain parameter should be nance frequencies 2 = n0 1, an increase in magnitude taken into account only at |γ| Ӷ ω . Otherwise, they σ ω ω 1 of the negative dissipative SL conductivity ( 2, g1, 1) should be dropped and, for convenience, we put n0 = 0 at the frequency of a weak signal is observed [4, 7]. in the rest of the sum. These narrow resonance regions of weak-signal ampli- A comparison of Eqs. (11) and (12) reveals the fol- fication are parts of rather broad regions of the negative σ ω ω lowing features of BOs in the macroscopic current. conductivity ( 2, g1, 1). Figure 1 shows the regions (1) As in the case of a static field [6], the shift of the of negative dc conductivity and high-frequency con- ±ω ductivity at the frequency ω of the strong field for ωτ = BO spectrum by 2 can be considered as an amplitude 1 modulation of the main spectrum (10) with frequency 10. The boundaries of regions 2 (heavy lines) corre- ω γ spond to the states with a zero steady-state current 2 or . However, now this modulation does not have a random phase and, hence, is not suppressed by colli- (heavy solid segments correspond to the stable states, sions and the current spectrum contains all three sets of and dashed and thin solid segments along the abscissa BO frequencies. (In the case of a static or harmonic axis correspond to the unstable states), and the bound- field, the spectra for a steady-state current and BOs dif- aries of regions 1 (thin lines) correspond to the states fer [6].) with a zero alternating current. Dot-and-dash curves γτ ӷ (ovals) correspond to zero differential dc conductivity (2) If 1, then all harmonics of BOs are high-fre- of the SL (this conductivity is negative inside the quency and the BO eigenfunction averaged over high- ovals). Due to the high negative values of conductivity ψ ≅ ν σ ω ω | ω frequency oscillations is ν (t) J0( g) = const. There- ( 2, g1, 1) near the resonance frequencies (at n 1 Ð ω | Շ τÐ1 fore [see Eqs. (7), (9)], just as in the case of one har- 2 ), effective parametric amplification of cou- monic field, the macroscopic current differs from BOs pled Stokes and anti-Stokes oscillations occurs at fre-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 160 ROMANOV, ROMANOVA

4 ψν (t) ≈ const (and is complex), the SL remains transparent and the weak signal is not ampliﬁed, collapse of 1 δ π the quasi-energy minibands [for even n0 and 0 = n or 3 δ π for odd n0 and 0 = (n + 1/2) ] takes place. At arbitrary

1 δ values of 0, IT is absent in the SL. The parametric ω 122 /

2 1 ampliﬁcation and the generation of harmonics of the ω

, strong ﬁeld are a second substantial channel of SIT sup-

1 2 ω

/ pression in the SL. C ω ӷ ω ≤ τÐ1 Ω (6) The case of 1 2 (n0 = 0) is specific, 1 since the field frequency coincides with that of a low- frequency harmonic of BOs, which is heavily sup- 2 pressed by collisions. Therefore, the degree of BO coherence and the collision-induced change in modula- 0 192 3 4 5 6 7 8 10 tion of the BO spectrum are proportional to the same Ω ω function J0(g1). At J0(g1) = 0, both processes are absent 1/ 1 and IT appears (see Eq. (12) at n0 = 0). It should be τ Fig. 1. Regions of negative conductivity for fields E noted that, beyond the = const approximation, IT also 1 does not appear in this case. (regions 1) and EC (E2 = 0) or E2 (EC = 0) (regions 2). ω τ ω ω 1 = 10. (7) In the case of the resonance 2 = n0 1, an additional velocity component caused by electron motion inside the quasi-energy minibands appears in Eqs. (10) ω ≈ ω ± τÐ1 τ quencies 2, 3 n1, 2 1 (n1, 2 = 1, 2, …), which is and (11) for BOs. For even values of n0 at t < , this one of the main channels of SIT suppression. induces a significant rectified current γ ∂ε() (5) In the case of exact resonance ( = 0), the current ne ˜ k3 ω ω ӷ τÐ1 j ==------j J ()g g sinδ . (14) at the frequency 2 = n0 1 is equal to C ប ∂ 0 n0 1 2 0 k3 0 {[]ω2() 2 () ()δ However, in time τ, collisions suppress this current to a jω = j0g2 J0 g1 Ð Jn g1 sin 2t + 2 2 0 ω τ Ð1 δ small value ~( 1 ) An (g1)cos 0 [see Eq. (12)], which n 0 Ð []J ()g J ()g Ð ()Ð1 0 J 2 ()g 0 1 2n0 1 n0 1 is totally specified by transitions between the quasi- n energy minibands. Similarly to absorption in a har- ×ωsin()t + δ Ð 2δ } + j ()11Ð ()Ð 0 monic field, this rectified current is relatively high in 2 2 0 0 (13) δ ± π the region J0(g1) = 0 and 0 = n but appears after the × J ()g J ()g sin() ωtn+ δ --- time ~τ, since the rectified current in BOs [see Eq. (14)] 0 1 n0 1 2 0 1 is absent in this case. ≈ 1 (8) At J0(g) 0, the SL has an absolute negative con- + ------A ()g cos() ωtn+ δ , ductivity (ANC) (Fig. 1, region 2) in a broad band of ω τ n0 1 2 0 1 1 Ω ≤ ω static fields 0 < C 1. This effect was predicted in [2Ð4] and observed experimentally in [11]. ANC is that is, it contains additional terms caused by the para- another cause of suppression of the SL transparency metric resonance of the order 2n0 (the second term) and and manifests itself as the generation of divergent by the generation of the nth harmonic of the strong field σ ω ω plasma oscillations [7, 12], which result in the sponta- (the last term). Since the conductivity ( 2, g1, 1) is neous appearance of a significant static electromotive almost purely imaginary in this case, the amplification force in the SL [3, 4, 7]. of the weak signal is mainly determined by parametric resonance. At an odd value of n0, the parametric generation of a harmonic of the strong field occurs [10]. This 4. POSSIBLE STABILIZATION process has a hybrid character and includes the ordi- OF TRANSPARENCY STATES nary generation of the harmonic and its subsequent Thus, the SIT state in the SL in a harmonic field is continuous parametric amplification. Because of colli- unstable to the generation of both static and additional sions, this generation also exists at J0(g1) = 0, i.e., under harmonic fields. A static field is usually generated, since the conditions of DL. In the presence of a static field, the corresponding increment increases rapidly with the which appears, e.g., when SIT is suppressed, the para- field value (Fig. 2) [7]. We will show that an SL trans- metric generation of harmonics exists at all integer val- parency state can be stabilized by a second harmonic ues of n0 and the parametric amplification, at half-inte- field with a frequency close to that of the first field. ger values of n as well. The corresponding conductiv- To estimate the required field amplitudes and frequen- 0 |γ| Ӷ ω ities are given in [4, 7]. Since, for exact resonance cies, we consider the case of 0 < 1 (see case (3)

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 DESTRUCTION AND STABILIZATION 161

0 1 2 3 0 1 2 3 of the manifestation of BOs in a macroscopic current) under the assumption that the ﬁeld E is small but ﬁnite 0.08 2 0.3 (g2 < 1) and that n0 = 1. Owing to parametric mixing 0 0

j j ω µ ω ± ω µ ω ± γ / / and decay of the type = 2 = (2 + 1) ,

j j 3 0 1 2 0 1 – – the current spectrum in the SL will contain the frequen- ω ω ω 0 0 cies 2 and 1, odd harmonics n 1, and their satellites with even values of n. The current at the combination 1.0 (a) ω ω ω ω frequencies is given by / 1 / 1 ∞ 0.5 n 0

j ∆ ≈ ()() ()()

/ jj0 ∑ 11Ð Ð J0 g2 J1 g2 j

– ∞ 0 n = Ð  J ()g J ()g ×  () () 1 1 n 1 J0 g1 Jn Ð 1 g1 Ð ------2 - –0.5  1 + ()γτ (15) 0 4 8 200 210 220 230 × sin()()nω + γ t Ð δ ω π 1 n 1t/2 γτ  ()() ()()ω γ δ + J1 g1 Jn g1 ------cos n 1 + t Ð n . 0 (b) 1 + ()γτ 2  C g –0.5 This current vanishes at the zeros of J0(g2) and J1(g2). In Eq. (15), unlike in Eq. (12), we kept the Bessel functions that involve the amplitude of the “weak” ﬁeld E2; –1.0 however, for the sake of simplicity, only its fundamental harmonic is retained. The SL dc conductivity in a 0 100 200 300 biharmonic ﬁeld is ω t/2π 1 ∞

σ ()Ω ,,,Ω Ω ω = ∑ Jµ ()g Jµ ()g C C 1 2 1 1 1 2 2 Fig. 2. Setting-in of a stationary static field in an SL with a µ = Ð∞ low electron concentration exposed to a harmonic field. 12, (16) (a) Time evolution and spectra of the current (in the insets) Ω ++µ ω µ ω ωτ × C 1 1 2 2 and (b) the time evolution of the mean field. = 10 and ------2 2. ω ω 2 1 + ()Ω ++µ ω µ ω τ ( 0/ 1) = 0.05. C 1 1 2 2

0.04 1.5 4 4 2 1.0 2

g 3 1 0 0.5 2 1 0 ω

3 / σ 2 / C

C –0.1 0 0.1 Ω σ γ/ω 2 2 –0.04 1 2 1 2 1 1 –0.08 0 2 4 6 8 10 0 0.1 0.3 0.5 Ω ω 1/ 1 gC

Fig. 3. Static conductivity of the SL in a biharmonic field near the SIT state of the first field at (1) g2 = 0, (2) 0.1, (3) 0.25, and (4) 0.3. γ = 0.03ω. The inset shows the region Fig. 4. Instability regions 2 of the static field in the presence σ γ γ ω ω τ C > 0 on the plane of the weak field parameters ( , g2). g1 = of a biharmonic field for g2 = 0.3, = 0.025 1, and 1 = 2.405. 10. In regions 1, the static field is stable.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 162 ROMANOV, ROMANOVA

11 (a) (b) (c) 0.08 2 0 0 j j / / j j 0 0 g – – 0.04 1

–1 ~ ~ –1 0 50 100 150 3000 0 1 3 5 0 1 3 5 ω ω ω ω ω 1t / 1 / 1

˜ ω ω ωτ ω ω 2 Fig. 5. Stable SIT state in a biharmonic ﬁeld with V0 = 2.526, 2 = 1.05 1, = 10, and ( 0/ 1) = 0.05. (a) Current oscillogram, eV ˜ 0 (b) current spectrum, and (c) voltage spectrum. V0 = ------បω ()- , where CS is the linear SL capacitance. N 1 1 + CS/C1

Formula (16) is valid for a biharmonic field with arbi- 2.526.2 As can be seen from Fig. 5, an SL transparency trary amplitudes but incommensurable frequencies state (small currents of ~0.08 at the fundamental har- ω ≠ ω (n1 1 n2 2). The conductivity (16) is shown in Fig. 3. monic, of ~0.04 at the third harmonic, and of even ω ± γ As shown above, in a purely harmonic field (E2 = 0), the smaller values at the combination harmonics 2 1 ) τ dc conductivity at small EC is negative in the SIT “win- appears after time ~ and then persists. In a purely har- dows” (i.e., ANC appears). However, as an additional monic field with the same parameters (Fig. 2), the trans- harmonic field E2(t) (with the corresponding fre- parency state is broken within ~200 field-oscillation quency) appears, the energy of the first field is trans- periods and then a significant static field with gC ~ 1 and ferred not only to the static but also to the second field. currents of ~0.3 at the first-, second-, and third-har- The transferred energy increases with E2. As a result, monic frequencies appear. As shown by numerical cal- beginning from a certain value of the field amplitude culation, similar stabilization of a transparency state in E , the conductivity σ (Ω , Ω , Ω , ω ) becomes posi- the SL takes place in a multifrequency field whose 2 C C 1 2 1 ω tive (only the severe mode of exciting a static emf is spectrum lies in a narrow frequency band near 1 retained). Figure 3 (inset) shows the region of positive (∆ω ≈ τÐ1). σ Ω γ values of C( C 0) in the ( , g2) plane. Note that this region of parameters is not completely equivalent to the region of a stable transparency state, since at γ 5. CONCLUSIONS 0 the SIT also disappears (the characteristic fre- ω quencies are the values of 2 corresponding to the step (1) The IT effect can appear in a weakly dissipative ω ω ≈ SL placed in a high-frequency harmonic field (ωτ ӷ 1) 2/ 1 1). Figure 4 shows how the static-field instability regions displayed in Fig. 1 vary when the SL is addi- only in cases where (a) the fields applied to the SL have ω | ω ω | ӷ τÐ1 ± tionally exposed to a second relatively weak harmonic high frequencies ( 1, 2, n 1 Ð 2 , n = 1, 2, …) ω ӷ ω ≤ τÐ1 field (g2 = 0.3). It is seen that ANC disappears at EC = 0 or (b) 1 2 . and shifts toward high static fields. (2) The causes of the breaking of transparency states It is easy to show that the instability regions of a in the SL are (a) an increase in magnitude of the nega- static field in the presence of a biharmonic field with tive dissipative conductivity near resonance frequen- incommensurable frequencies are also regions of linear cies (|nω Ð ω | Շ τÐ1), which results in effective para- ω 1 2 instability of a third harmonic field with a frequency 3 metric amplification of coupled Stokes and anti-Stokes ω ω Ω ω that is not a multiple of 1 and 2 (with C/ 1 replaced oscillations (with frequencies ω ≈ n ω ± τÐ1, i.e., ω ω ≈ 2, 3 1, 2 1 by 3/ 1). Thus, the regions of J0(g1) 0 can become with frequencies that are close but not equal to multi- stable to weak (gC < 0.1 in the given example) fluctua- ples of the external-field frequency); (b) the parametric tions of the static field and to low-frequency perturba- amplification and generation of harmonics of the exter- tions in the presence of a biharmonic field with certain nal field; and (c) absolute negative conductivity, which parameters. As an example, Fig. 5 shows numerically leads to the spontaneous generation of significant static calculated internal voltage and current in an SL which fields. is connected to a dc open circuit and to which an exter- ω 2 nal biharmonic voltage V(t) = V0[sin( 1(t) + The equivalent circuit and the corresponding equation can be ω ω ω ˜ found in [7]. This circuit contains an N-period SL, an exterior 0.1sin( 2t)] is applied with 2 = 1.05 1 and V 0 = capacity C1, and a voltage source.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 DESTRUCTION AND STABILIZATION 163

(3) Transparency states that occur in an SL exposed 4. L. K. Orlov and Yu. A. Romanov, Fiz. Tverd. Tela to a biharmonic field with arbitrary amplitudes are also (Leningrad) 19 (3), 726 (1977) [Sov. Phys. Solid State unstable. In a biharmonic field with frequencies close 19, 421 (1977)]; Yu. A. Romanov, V. P. Bovin, and to each other (if the amplitude of one of the field com- L. K. Orlov, Fiz. Tekh. Poluprovodn. (Leningrad) 12, ponents is relatively low), the SL can be in a transpar- 1665 (1978) [Sov. Phys. Semicond. 12, 987 (1978)]. ency state stable to low-frequency fluctuations. 5. M. C. Wanke, A. G. Markelz, K. Unterrainer, et al., in Physics of Semiconductors, Ed. by N. Scheffter and R. Zimmerman (World Sci., Singapore, 1996), p. 1791. ACKNOWLEDGMENTS 6. Yu. A. Romanov and Yu. Yu. Romanova, Fiz. Tverd. Tela (St. Petersburg) 43 (3), 520 (2001) [Phys. Solid State 43, This work was supported by the Russian Foundation 539 (2001)]. for Basic Research (project no. 01-02-16446), the Min- 7. Yu. A. Romanov and Yu. Yu. Romanova, Zh. Éksp. Teor. istry of Industry and Science of the Russian Federation, Fiz. 118 (5), 1193 (2000) [JETP 91, 1033 (2000)]. and the Russian Academy of Sciences program “Low- 8. O. N. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 Dimensional Quantum Structures.” (1986); Phys. Lett. A 127, 438 (1988). 9. M. Holthaus, Z. Phys. B 89, 251 (1992); M. Holthaus REFERENCES and D. Hone, Phys. Rev. B 47, 6499 (1993). 10. Yu. A. Romanov, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 1. Yu. A. Romanov, Fiz. Tekh. Poluprovodn. (Leningrad) 5, 23, 617 (1980). 1434 (1971) [Sov. Phys. Semicond. 5, 1256 (1971)]; Opt. Spektrosk. 33, 917 (1972). 11. B. J. Keay, S. Zenner, S. J. Allen, et al., Phys. Rev. Lett. 75, 4102 (1995). 2. A. A. Ignatov and Yu. A. Romanov, Fiz. Tverd. Tela 12. Yu. A. Romanov, Fiz. Tverd. Tela (Leningrad) 21 (3), (Leningrad) 17 (11), 3388 (1975) [Sov. Phys. Solid State 877 (1979) [Sov. Phys. Solid State 21, 513 (1979)]. 17, 2216 (1975)]. 3. A. A. Ignatov and Y. A. Romanov, Phys. Status Solidi 73, 327 (1976). Translated by K. Shakhlevich

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

On a Superlattice Bloch Oscillator Yu. A. Romanov and Yu. Yu. Romanova Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected]

Abstract—The differential dc and hf conductivities of semiconductor superlattices with various electron miniband dispersion relations are studied. It is shown that, due to the anharmonicity of Bloch oscillations, the hf conductivity can be negative at frequencies equal to integral multiples of the Bloch frequency. This effect can arise even in the regions where the differential dc conductivity is positive. The results of the study suggest that superlattices with a miniband dispersion law in which the effective electron mass is positive in a sizable part of the miniband and decreases as the electron energy increases can be used to generate and amplify terahertz-range (microwave) ﬁelds. © 2004 MAIK “Nauka/Interperiodica”.

In semiconductor superlattices (SLs), the quasi- longitudinal and transverse effective masses. Due to the momentum Brillouin zones and the allowed electron existence of such regions (whose size and position in energy bands of the original homogeneous materials the SL Brillouin zone can be controlled), the SLs offer break up into relatively narrow (105Ð107 cmÐ1) Bril- promise as NEMAG-like radiation sources [2]. louin minizones and narrow (10Ð3Ð10Ð1 eV) allowed Bragg reflections and negative effective electron and forbidden energy minibands. Because of the small- masses are the reason for the occurrence of negative dc ness of these minibands, electron Bloch oscillations and hf (dynamic) differential conductivities (NDCs) in (BOs) occur and WannierÐStark energy levels arise in SLs. In an SL with sine minibands, these conductivities an SL even in relatively weak static electric fields (102Ð become negative simultaneously and in the same range Ω τ τ 104 V/cm). The BOs are characterized by the Bloch of strong electric fields for which C > 1 ( is the elec- Ω ប (WannierÐStark) frequency C = eECd/ and the quasi- tron velocity relaxation time). Therefore, terahertz- classical amplitude of spatial oscillations Z = ∆/2eE , range oscillations in such SLs are suppressed because C C of the development of relatively low-frequency domain where EC is the strength of a static electric field applied along the axis of the SL with a spatial period d and instability. These oscillations can occur in a semicon- energy miniband width ∆, e is the electronic charge, ductor SL whose currentÐvoltage (IÐU) characteristics have a range over which the dc differential conductivity and ប is the Planck constant. In the case of d = 100 Å ≡ Ω π ≈ is positive and the hf differential conductivity is nega- and EC = 4 kV/cm, the BO frequency is fC C/2 1 Ω tive. Such a situation can be realized in several different THz. It is important that the Bloch frequency C is ways: (i) by displacing the range of negative values of independent of the miniband dispersion law and is the dc differential conductivity toward high fields determined only by the SL period and the electric field Ω τ ( C > 1) while preserving the negative hf differential strength in the SL. The miniband dispersion relation conductivity in lower fields; (ii) by displacing the range manifests itself in the anharmonicity of spatial oscilla- of negative hf differential conductivity toward low tions of electrons. In the case of the conventionally Ω τ static fields ( C < 1) while leaving the static IÐU char- assumed sine dispersion law, these oscillations are har- acteristic unchanged or, in general, by separating the monic. The existence of BOs in SLs has been convinc- electric-field ranges of negative dc and hf differential ingly confirmed in a number of experiments, and their conductivities; or, finally, (iii) by “opening” an addi- anharmonicity has also been observed experimentally. tional channel for the direct current to flow in a narrow These facts suggest that semiconductor SLs can be used range of static electric fields where the hf differential to develop a terahertz Bloch oscillator whose frequency conductivity is negative (i.e., at the “operating point”). can be continuously tuned by a static electric field [1]. To attain these ends, we can vary the dispersion rela- Another important feature of the SL is the presence tions in the electron energy minibands [3], turn on or of regions with a negative effective electronic mass in off (weaken) certain electron scattering mechanisms the SL Brillouin zone. These regions may be of consid- (especially those involving optical phonons), or make erable size. For example, in the case of a sine dispersion use of electron tunneling between minibands [4]. This law, the effective electron mass is negative in one half work is dedicated to the issues outlined above. of the SL Brillouin zone. In minibands of two- and In order to elucidate the mechanisms of the occur- three-dimensional SLs, there are regions with negative rence of NDC in an SL and the possibility of control-

ON A SUPERLATTICE BLOCH OSCILLATOR 165 π/d] and, reaching the SL Brillouin boundary (k = π/d), ling it, we consider the simple case of one miniband 3 undergoes specular reflection from it (thereby hopping with an additive electron dispersion law: π to the point k3 = Ð /d) and, continuing in motion against ប2 2 the field, reenters the passive region without emitting ε() ε()ε() ε () k⊥ k ==3 k3 + ⊥ k⊥ , ⊥ k⊥ ------, (1) an optical phonon or (2) the electron, moving in the 2m active region, emits an optical phonon with a probabil- α where ε(k) and k are the energy and quasi-wave vector ity (k⊥, EC) and transfers to the region of energies ε ε ε ≈ of an electron, respectively; 3(k3), k3 and ⊥(k⊥), k⊥ are (k) 0. According to the energy conservation law, the their longitudinal and transverse components (with transverse momentum of the electron decreases (the respect to the SL axis), respectively; and m is the effec- electron momentum can remain unchanged only when tive transverse electron mass. We consider the follow- a phonon is emitted exactly at the miniband edge k3 = ing two qualitatively different dispersion laws for the π/d. Then, all the processes described above repeat ε longitudinal energy 3(k3): (i) a sine law again and again. As a result, the transverse electron momentum k⊥ 0 and its steady-state distribution ∆ ε () []() becomes a needle-shaped distribution described by a 3 k3 = --- 1 Ð cos k3d (2) 2 superposition of two Baraff functions [6], in which case, as mentioned above, the effective elec- 2 2 f ()k = 8π ndδ ()k⊥ tron mass is negative in one half of the SL Brillouin C (4) zone, and (ii) a “superparabolic” (idealized) law α()θ, ()π []θπα(), () × 0 EC k3 Ð /d + 1 Ð 0 EC /dkÐ 3 ------α(), , 2 << 2 Ð 0 EC k2 /m1,0 k3 ki ប2 θ α ε() 2 where (x) is a theta function, (0, EC) is the effective k3 = ----- k /m Ð 2k ()1/m Ð 1/m ()k Ð k /2 2  3 2 i 2 1 3 i optical-phonon emission probability for an electron  <<π (3) with transverse quasi-wave vector k⊥ ≈ 0, and n is the ki k3 /d, electron concentration. The time required for this distri- which consists of two parabolas matched at the points bution to set in increases with decreasing scattering ± π π α k3 = ki, where 0 < ki < /d. If m2 = m1 or ki = 0 ( /d), probability (k⊥, EC). Eq. (3) reduces to a parabolic dispersion relation, while π The formation of an anisotropic free-carrier in the case of m2 = Ðm1 < 0 and ki = /2d Eq. (3) momentum distribution that is highly extended along becomes a reasonable approximation to the sine disper- the electric field direction in a semiconductor is sion law given by Eq. (2). It is very significant that, in a α referred to as streaming [7]. For (0, EC) = 1 (the abso- miniband with dispersion law (3) with m1, 2 > 0, regions lutely rigid phonon “roof”), expression (4) reduces to a with a negative effective mass are absent and there are ±π usual needle-shaped Baraff function [6] describing the only Bragg reflection points k3 = /d at the boundaries hot-electron distribution in homogeneous semiconduc- of the SL Brillouin zone. We are particularly interested tors in the case of ideal streaming (τ = 0, τ ∞). ӷ 0 in dispersion relation (3) with m1 m2 > 0, i.e., in mini- Clearly, BOs do not arise in this case and, hence, no bands in which the effective electron mass decreases effects characteristic of SLs are observed (except a pos- with increasing electron energy. Such a dispersion law sible specific electron dispersion law with, in particular, takes place in hole quantum layers [5]. τ ≠ regions of negative effective masses). For 0 0, the We use the following physical model to consider the electron momentum distribution in homogeneous semi- dynamics of an electron in the SL and its scattering by conductors expands in both the longitudinal and trans- optical phonons in the presence of a static electric field. verse directions (with respect to the applied electric It is assumed that the SL miniband width ∆ is approxi- field) because of the penetration of electrons into the បω mately equal to the energy of an optical phonon 0 active region [8]. τ and that the phonon emission time 0 by an electron is The streaming in SLs has specific fundamental fea- much shorter than the other relaxation times, in partic- tures: τ Ӷ τ ular, 0 . If in the so-called passive quasi-momen- ε បω (1) The depth of penetration of an electron into the tum range [where (k) < 0] there is no electron scat- active region is mainly determined by the position of Ω τ ∞ បω ∆ tering ( C ) and 0 = , then an electron with the miniband top rather than by the optical-phonon ε បω energy ⊥(k⊥) < 0 moves in quasi-momentum space emission probability. Therefore, the streaming in an SL at a constant velocity until its energy becomes equal to is narrower than that in the corresponding bulk mate- ε បω (k) = 0 and its longitudinal quasi-wave vector is rials. ()0 equal to the corresponding value k (k⊥) ≤ π/d. There- (2) If the optical-phonon emission probability 3 α after, the following alternatives are possible. (1) Either (0, EC) < 1, then two-sided streaming occurs in an SL; the electron transfers to the so-called active region of that is, the momentum distribution function is needle- shaped and is nonzero not only for positive but also for ε បω ()0 | | ≤ quasi-momentum space [ (k) > 0, k3 (k⊥) < k3 negative values of the electron quasi-momentum.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 166 ROMANOV, ROMANOVA

(3) The quasi-momentum dependence of the elec- We will assume these times to be equal and will desig- tron velocity is nonlinear, which significantly affects nate each of them as τ. Since the phase volume is rela- the character of the SL conductivity. tively small, the probability of electron scattering α without leaving the trap is small and such scattering In the case of one-sided streaming [ (0, EC) = 1], the electron motion is a combination of periodic motion at can be approximately taken into account in collision Ω integral (5) by slightly decreasing the time τ. frequency 2 C and translation (in coordinate space) ∂ε() (2) Since collisions in the passive region are π/d k3 Ω τ with velocity 〈V〉 = (d/πប) ------dk . Under the assumed to occur rarely ( C > 1), the number of ∫0 ∂ 3 k3 untrapped electrons is small (Ω τ times smaller than α C conditions of two-sided streaming [ (0, EC) < 1], the that of trapped electrons). The untrapped electrons electron motion is characterized by two frequencies make a small, nonresonant contribution to the hf cur- Ω Ω ( C, 2 C) and by the average translation velocity, rent. For simplicity, we neglect this contribution and α which is (0, EC) times lower than that for one-sided put n(t) = n = const in Eq. (5). streaming. (3) Since the cylindrical region in which electrons បω տ ∆ are trapped is narrow, we will assume that the trapped The case of 0 is of importance. In this case, the electrons that are scattered into a cylindrical domain electrons emit optical phonons with the same effective α δ ≈ ()បω ∆ probability (independent of k⊥) when they are located of radius k 2m 0 Ð in quasi-momentum π exactly at the miniband edge (at the point k3 = /d). To space are trapped and reside in this domain for an infi- simplify the analysis of the results, we assume that this nitely long time, because they are not scattered by opti- probability is also independent of the applied electric cal phonons. Therefore, such electrons are accumulated field. with time after the electric field is switched off. How- Under these assumptions, the electron distribution ever, as the electric field is increased, optical-phonon function f(k3, t) integrated over k⊥ is determined in the emission by electrons with smaller values of បk⊥ also range Ðπ/d < k < π/d using the one-dimensional Boltz- becomes possible (due to the tunneling effect); the 3 domain where electrons are trapped narrows (to a cer- mann equation tain size) and its boundary becomes diffuse (but to a ∂fk(), t eE() t ∂fk(), t ------3 + ------3 smaller extent than in homogeneous semiconductors). ∂t ប ∂k In this domain, electrons are mixed but do not leave it 3 (6) when they emit optical phonons. fk(), t Ð 2πnδ()k eE() t = Ð------3 3- + α------f ()δπ/dt, ()k Now, let us discuss the part played by quasi-elastic τ ប 3 electron scattering in the passive region. In general, this scattering can be taken into account only by using with the boundary condition numerical methods (e.g., the Monte Carlo method). f ()Ðπ/d, t = ()1 Ð α f ()π/dt, . (7) Since our aim is to investigate the hf conductivity of an SL in a qualitative way, we make several simplifying In Eq. (6), the terms involving delta functions can be assumptions in order to solve the problem analytically. treated as point sources of electrons and describe optical-phonon scattering of electrons. In solving this (1) We assume that the phonon roof is rigid, i.e., that (homogeneous) equation separately in the ranges (Ðπ/d, δ the penetration depth of electrons with k⊥ > k into the 0) and (0, π/d), these terms can be conveniently active region is infinitely small. (In this case, the prob- replaced by the condition of conservation of the num- α ability (0, EC) can be much less than unity.) Under ber of particles these conditions, due to quasi-elastic scattering, a π/d trapped electron will leave the “trap” and be accelerated dk fk(), t ------3 = n (8) by the electric field; having reached the boundary of the ∫ 3 2π active region, the electron will emit an optical phonon Ðπ/d and revert rapidly to the state with energy ε(k) ≈ 0. With allowance for the conservation of the number of parti- or by the corresponding boundary condition at the point cles, these processes can be described approximately k3 = 0, which is obtained by integrating Eq. (6) over a by the collision integral vicinity of the point k3 = 0. Equation (6) corresponds to the commonly used fkt(), Ð ()2π 3nt()δ3()k Drude model, which assumes that, in any collision (in ------τ -, (5) the passive region), an electron transfers to the state of C zero energy and that the collisions are characterized by where f(k, t) and n(t) are the distribution function and the relaxation time τ. When using this model, we need τ concentration of trapped electrons, respectively, and C not take into account the assumptions made above. τ Ω τ is the lifetime of an electron in the trap. The time C is Therefore, we will also use Eq. (6) in the case of C < 1 close to the electron velocity relaxation time τ intro- and include all particles, rather than only trapped ones, duced above (not including optical phonon scattering). in the distribution function f(k3, t). We realize that this

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 ON A SUPERLATTICE BLOCH OSCILLATOR 167

5 5 0.6 5 4

4 0.4 4

0 3 j 0 / j / C j C j 3 3 2 0.2 2 2 1 1 1

0 2 4106 8 0 2 486 Ω τ Ω τ C C

Fig. 1. IÐU curves of an SL with a sine miniband dispersion law for various values of the probability α of optical- Fig. 2. IÐU curves of SLs with a superparabolic miniband η ≡ β ≡ π phonon emission by electrons at the miniband edge: (1) 0, dispersion law for m1/m2 = 10 and kid/ = 0.5. (2) 0.25, (3) 0.5, (4) 0.75, and (5) 1. Labeling conventions are the same as those in Fig. 1.

τÐ1 approximation is fairly crude and can give only a qual- fC(k3, ) is the electron distribution function in a static itative description of the results. field, and Within the model described above, we find the elec- (),,τÐ1 (), τÐ1 ()ω f 1 k3 t = f 1 k3 exp Ði t , tron distribution function and the conductivity of an SL (), τÐ1 ()ωτ () in the field f 1 k3 = i/ E1/EC (12) × [](), τÐ1 (), τÐ1 ω () ()ω f C k3 Ð f C k3 Ð i Et = EC + E1 cos t , (9) is the variation of this function caused by a weak har- where the static-field strength can have an arbitrary monic field. Therefore, the dynamic differential con- value, while the amplitude of the harmonic field satis- ductivity σ(ω, τÐ1) is related (in the approximation at Ӷ ប|ω τÐ1| σ τÐ1 fies the condition E1 + i /ed; therefore, we hand) to the total dc conductivity C( ) by the relation consider an approximation linear in E . For the sake of 1 σωτ(), Ð1 = ()σi/ωτ []()στÐ1 Ð ()τÐ1 Ð iω . (13) convenience, we introduce an additional argument, the C C inverse relaxation time τÐ1, in the distribution function The conductivities introduced above are defined by the and conductivity. In this notation, the solution to Eq. (6) conventional relations between the current density j(t) with conditions (7) and (8) has the form and the field E(t) π /d ∂ε (),,τÐ1 (), τÐ1 (),,τÐ1 e ()k3 , dk3 ω ()ω fk3 t = f C k3 + f 1 k3 t , (10) jt( ) = ប--- ∫ ------∂ fk()3 t ------π = jC + j1()exp Ði t , k3 2 Ðπ/d (14) where σ ()ω σω()()ω jC ==CEC, j1 E . π (), τÐ1 2 nd We note that distribution functions (11) and (12) f C k3 = ------Ω τ- C found by us are independent of the miniband dispersion law. This feature significantly alleviates the problem of k d exp Ð------3 - elucidating the part played by the dispersion law in the Ω τ occurrence of the NDC in an SL. This circumstance × ------C - π π justifies using the crude approximation described ()α above. It can be shown that Eqs. (12) and (13) are also 1 Ð11expÐΩ------τ- + Ð expÐΩ------τ- (11) C C valid under less restrictive assumptions. Now, we present the IÐU curves and dynamic con- 1, 0 <

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 168 ROMANOV, ROMANOVA

2 0 σ

)/ 0.2 ω

( 0.1

σ 0.1 Re

0 1 3 2 4 6

σ 0 3 )/

ω Ω 0 / C ω 2 σ

( 0 )/ σ

1 ω 2 ( Re 0 σ 1 Re –0.1

–1 0 2 46 ω Ω – 0.2 / C 0 2 46 ω Ω / C Fig. 3. Dynamic SL conductivities for a sine (inset) and a superparabolic miniband dispersion law with β = 0.5 and Fig. 4. Dynamic SL conductivities in the case of a superpa- different values of η: (1) 1, (2) 5, and (3) 10; α = 0 and rabolic dispersion law for various values of α: (1) 0, (2) 0.5, Ω τ Ω τ β η C = 1. and (3) 1; C = 10, = 0.5, and = 10. culated for different values of the probability α of opti- differential conductivity becomes negative at frequen- cal-phonon emission by an electron at the miniband cies equal to integral multiples of the Bloch frequency edge (more detailed results can be found in [3]). It can even in fields for which the dc differential conductivity be seen from Figs. 1 and 2 that the existence of regions of the SL is positive. At α = 0 (Fig. 3), a necessary con- ω Ω τÐ1 with negative values of the effective electron mass in dition for this effect to occur is ~ n C > (n = 2, 3, the miniband is not a necessary condition for the dc dif- …); that is, the spread of the nth BO harmonic must be ferential conductivity to be negative. This conductivity small, whereas the spread of the fundamental harmonic Ω τ η can be negative even in SLs with parabolic and super- can be strong, C < 1. As the value of is increased, parabolic miniband dispersion laws (for which the the dynamic NDC increases in magnitude. In SLs with effective electron mass is positive everywhere), and its a sine dispersion law, higher BO harmonics are absent; sign in these cases is dictated by Bragg reflections of therefore, the dynamic differential conductivity cannot electrons (Bragg reflections are more important, be negative in such fields. because they change the electron velocity direction, If the miniband width in an SL is of the order of the whereas a change in sign of the effective mass affects optical-phonon energy and the optical-phonon emis- only the magnitude of the electron velocity). When sion probability is large (α ≈ 1) at the transit frequency Bragg reflections of electrons are suppressed by optical (which is twice the Bloch frequency in the case in ques- phonons, the negative dc conductivity may disappear tion) and at its integral multiples (i.e., at the frequencies altogether. Such conductivity will persist only if the of even BO harmonics), then the dynamic NDC arises effective electron mass is negative in a sizable portion because of one-sided streaming and self-modulation of (usually, larger than one half) of the SL Brillouin zone the electron quasi-momentum distribution. The dc volume [3]. The desirable shift of the range of negative NDC may be absent in this case for any value of the values of the dc conductivity toward high static fields applied static field. This mechanism of the dynamic takes place when the effective electron mass decreases NDC is not related directly to BOs of electrons and is with increasing electron energy. For example, in the operative even in the absence of BOs. The existence of α absence of optical-phonon scattering ( = 0), the dc the dynamic NDC due to streaming and to electron dis- Ω τ conductivity becomes negative at C = 1 in SLs with tribution self-modulation in bulk semiconductors was Ω τ ≈ a sine miniband dispersion law, at C 1.17 in SLs predicted in [8] and observed experimentally in [9]. In Ω τ ≈ with a parabolic miniband, and at C 1.4 in SLs with the case of two-sided streaming, the dynamic NDC can β π the dispersion law given by Eq. (3) with = kid/ = 0.5 occur at frequencies of both even and odd BO harmon- η α and = m1/m2 = 10. When the optical-phonon scatter- ics. As the optical-phonon emission probability ing of electrons is strong, this shift is much larger than increases, the NDC decreases in magnitude at frequen- the values presented above. cies of odd BO harmonics and increases at frequencies of even BO harmonics (Fig. 4), because BOs disappear The dynamic SL conductivities for these electron as α 1. It is important that the resonance values of dispersion laws are shown in Figs. 3Ð5. It can be seen NDC arise on the left and on the right of the frequencies that, due to the anharmonicity of BOs (associated with of odd and even BO harmonics, respectively. This fea- the electron dispersion differing from a sine law), the hf ture is due to inversion of the partial electron distribu-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 ON A SUPERLATTICE BLOCH OSCILLATOR 169

static fields, whereas the range of dynamic NDC shifts 0.075 (a) Ω τ toward weak fields (becoming finite at C = 1) and increases in magnitude.

0 Thus, SLs in which the minibands are not sinusoidal σ

)/ 0.050 can be used to generate and amplify terahertz-range ω

( (microwave) ﬁelds with frequencies equal to integral σ multiples of the Bloch frequency in the regime where Re low-frequency domain instability is suppressed. Sys- 0.025 tems in which the effective electron mass decreases 1 with increasing electron energy are suitable for this purpose. Such dispersion laws can be realized in SLs 2 3 and two-dimensional hole-conduction layers. SLs with two closely spaced minibands are also appropriate if 0 2 486 the upper miniband is signiﬁcantly wider than the lower ω Ω / C one and optical phonons are emitted by electrons at the top of the upper miniband. 0.15 (b) ACKNOWLEDGMENTS 0.10 1 This study was supported by the Russian Founda-

0 tion for Basic Research (project nos. 01-02-16446, σ 02-02-17495), the Russian Academy of Sciences pro- )/ ω

( 0.05 gram “Low-Temperature Quantum Structures,” and the 2 σ Ministry of Industry, Science, and Technology of the Re 3 Russian Federation. 0 REFERENCES –0.05 1. L. Esaki and R. Tsu, IBM J. Res. Dev. 14, 61 (1970). 0 2 486 2. H. Kroemer, Phys. Rev. 109, 1856 (1958). ω Ω / C 3. Yu. A. Romanov, Fiz. Tverd. Tela (St. Petersburg) 45 (3), 529 (2003) [Phys. Solid State 45, 559 (2003)]. Fig. 5. Dynamic SL conductivities in the case of one-sided 4. L. K. Orlov and Yu. A. Romanov, Fiz. Tekh. Polupro- α Ω τ streaming ( = 1) for different values of C : (1) 3, (2) 5, vodn. (Leningrad) 19, 1877 (1985) [Sov. Phys. Semi- and (3) 10 for (a) sinusoidal and (b) parabolic minibands. cond. 19, 1157 (1985)]; Izv. Vyssh. Uchebn. Zaved., Radioﬁz. 32, 282 (1989). 5. Y. C. Chang and R. B. James, Phys. Rev. B 39, 12672 tions over Fourier components of the dispersion rela- (1989). tion in SLs with miniband dispersion relations differing 6. G. A. Baraff, Phys. Rev. 133, A26 (1964). from a sine law. It is worth noting that, in SLs with a 7. W. E. Pinson and A. Bray, Phys. Rev. 136, A1449 sine-law miniband, optical phonons suppress both the (1964). dc and dynamic NDCs over the entire frequency range 8. A. A. Andronov and V. A. Kozlov, Pis’ma Zh. Éksp. Teor. (Fig. 5). Generally, it can be shown that the existence of Fiz. 17, 124 (1973) [JETP Lett. 17, 87 (1973)]. ranges of negative values of the effective electron mass in the miniband has an adverse effect on the high-fre- 9. L. E. Vorob’ev, S. N. Danilov, V. N. Tulupenko, and D. A. Firsov, Pis’ma Zh. Éksp. Teor. Fiz. 73, 253 (2001) quency NDC caused by one-sided streaming and by [JETP Lett. 73, 219 (2001)]. self-modulation of the electron quasi-momentum distribution. From Figs. 1Ð4, it also follows that, as α and η increase, the range of dc NDC shifts toward high Translated by Yu. Epifanov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 17Ð21. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 21Ð25. Original Russian Text Copyright © 2004 by Tetelbaum, Gorshkov, Burdov, Trushin, Mikhaylov, Gaponova, Morozov, Kovalev.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) The Influence of P+, B+, and N+ Ion Implantation on the Luminescence Properties of the SiO2 :nc-Si System D. I. Tetelbaum*, O. N. Gorshkov*, V. A. Burdov*, S. A. Trushin*, A. N. Mikhaylov*, D. M. Gaponova**, S. V. Morozov**, and A. I. Kovalev*** * Physicotechnical Research Institute, Nizhni Novgorod State University, pr. Gagarina 23/3, Nizhni Novgorod, 603950 Russia e-mail: [email protected] ** Institute of Microstructure Physics, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia *** Bardin Central Research Institute of Ferrous Metallurgy, Vtoraya Baumanskaya ul. 9/23, Moscow, 107005 Russia

Abstract—The possible mechanisms of the inﬂuence of implanted impurities of Group III and V elements on the luminescence properties of a system consisting of silicon nanocrystals in SiO2 are considered and general- ized. The effect of boron and nitrogen ion implantation on the photoluminescence intensity is investigated experimentally. The experimental results and previously reported data on the ion-implantation doping with phosphorus are discussed in terms of the mechanisms under consideration. The state of implanted phosphorus is determined using x-ray photoelectron spectroscopy. It is shown that the enhancement and degradation of the photoluminescence depend on the type of implanted impurities and the conditions of postimplantation heat treatment. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION luminescence and presented new experimental evi- In recent years, systems consisting of nanocrystal- dence in support of these particular models. line silicon inclusions in silicon dioxide (SiO2:nc-Si) have attracted considerable attention of many research- 2. MAIN FEATURES OF THE INFLUENCE ers due to the manifestation of quantum-size effects OF SHALLOW-LEVEL IMPURITIES responsible for their unique combination of properties, ON THE PHOTOLUMINESCENCE such as luminescence in the visible and near-IR spectral regions, resonant tunneling, etc. The doping of The main photoluminescence band, which is associated with silicon nanocrystals in the SiO2:nc-Si system, SiO2:nc-Si has opened up new possibilities for modify- ing the electrical and optical properties of the system. is observed in the wavelength range 750Ð900 nm [8Ð However, there are only a few works concerned with 11]. At present, there exist two points of view regarding investigating the influence of impurity atoms (in partic- the origin of the photoluminescence band in this range. ular, shallow donors and acceptors) on the properties of According to the first approach [8–10], the photoluminescence is caused by the interband transition of an the SiO2:nc-Si system; moreover, the results obtained in those works are contradictory [1Ð7]. excited electron from the lower energy level of the conduction band (hereafter, it will be referred to as the c Ion implantation is a very convenient method for level) of a silicon quantum dot to the upper level of the introducing impurity atoms into a system. First, ion valence band (the v level). Within the second approach implantation is one of the most universally employed [11, 12], it is assumed that an excited electron from an processes of SiO2:nc-Si production; the synthesis and energy level of the conduction band first is nonradia- doping of the material can be performed both in combi- tively captured in an interfacial level (located at the nation and, if necessary, individually under specified interface between the silicon nanocrystal and the SiO2 temperature conditions of postimplantation annealing. matrix) and then emits a photon upon the transition to Second, ion implantation imposes little or no restric- either the v level or another interfacial level that has tions on the type and concentration of implanted impu- captured an excited hole from the v level. In both rities. approaches, the photoluminescence intensity is con- Earlier [5Ð7], we experimentally investigated how trolled by a competing process, namely, nonradiative the ion-implantation doping of the SiO2:nc-Si system recombination. Dangling bonds at the nc-Si/SiO2 inter- with phosphorus affects the photoluminescence (PL) face can serve as nonradiative-recombination centers. properties and compared the experimental data with the The currently available models of the influence of results of theoretical calculations. In the present work, impurity atoms on the photoluminescence can be sepa- we attempted to generalize several models describing rated into three groups. According to models of the first the influence of shallow-level impurities on the photo- group, the mechanism of this influence is associated

18 TETELBAUM et al. with the possibility of generating and annihilating non- transition is attended by emission or absorption of one radiative-recombination centers. Models of the second phonon, the reciprocal of the radiative recombination group allow for the transformation of the state of the time is characterized by a considerably smoother electronic system of nanocrystals as quantum dots, i.e., dependence on the quantum dot size [i.e., (a/r)3] and is the direct effect of impurities on the probability (rate) approximately equal to 106 sÐ1 at 2r = 3Ð5 nm. We cal- of radiative transitions. Models of the third group culated the probability of photon emission occurring describe the influence of dopants on the formation, with the participation of phonons when one hydrogen- structural state, and morphology of silicon nanoinclu- like donor atom is located at the center of the silicon sions upon ion implantation and subsequent annealing. quantum dot. According to these calculations, a slight Let us analyze these models in greater detail. increase in the recombination probability (by 10Ð15%) (i) The photoluminescence intensity should increase is associated primarily with the fact that the perturbing in the case where the introduction of impurity atoms potential of the impurity atom admixes higher energy leads to a decrease in the concentration of dangling states to the ground states of electrons and holes, bonds (nonradiative-recombination centers) at the nc- which, in turn, leads to an increase in the overlap of the Si/SiO2 interface. This decrease in the concentration of electron and hole wavefunctions in the k space. The nonradiative-recombination centers can result from a contribution of these states with a high energy for a sin- decrease in mechanical stresses (arising upon heat gle impurity atom is rather small. This explains the rel- treatment) because of the close values of the thermal atively small increase in the recombination probability. expansion coefficients of the silicon inclusions and the However, an increase in the donor concentration most likely results in a considerably greater increase in the SiO2 matrix [2]. However, the influence of implanted impurities of Group V elements on the photolumines- probability of the interband radiative transition and, cence intensity can be associated with another mecha- hence, in the photoluminescence intensity. nism of passivation [6] (by analogy with hydrogen) due (iv) Fujii et al. [1Ð3] made the assumption that the to the termination of dangling bonds with impurity incorporation of shallow-level impurities into silicon atoms. nanocrystals should lead to quenching of the photolu- (ii) In our previous works [5, 6], we proposed an minescence due to the Auger process. Earlier, this pro- electronic mechanism of photoluminescence enhance- cess was theoretically analyzed by Lannoo et al. [13], ment upon dissolution of donor atoms in silicon nanoc- who considered the situation where more than one exci- rystals. In essence, this mechanism is as follows. In the ton can appear in the quantum dot upon excitation. absence of donors, the excitation of photoluminescence However, the theory developed by those authors cannot requires excitation of an electron from the v level to the be directly extended to our case, because an excess conduction band, which leads to the creation of an exci- charge carrier introduced by an impurity atom resides ton. Upon dissolution of a donor atom in a silicon in the Coulomb field of the core of a donor or acceptor nanocrystal, this atom loses an excess electron to the impurity center, which was ignored in [13]. Indeed, the conduction band. In turn, this electron recombines with experiments performed in [14] demonstrated that no a hole created upon the transfer of an electron from the complete quenching of the photoluminescence occurs v level, which provides an additional photolumines- even through a large number of phosphorus atoms are cence channel. incorporated into each nanocrystal. (iii) Another electronic mechanism of doping effect (v) Kachurin et al. [14] proposed a mechanism of is also proposed for quantum dots. Since bulk silicon is photoluminescence enhancement upon ion-implanta- an indirect-band-gap semiconductor, the transition tion doping with phosphorus, which is based on the from the c level to the v level with photon emission, high-dose effect [15]. Within this approach, allowance generally speaking, is a forbidden transition due to the is made for the fact that, at high concentrations, momentum nonconservation in this process. However, implanted phosphorus impurities favor crystallization in a quantum dot, the electron state is characterized by of amorphous silicon. As a result, upon annealing, a momentum distribution with finite dispersion, which implanted phosphorus should bring about the transfor- provides a means for conserving the total momentum mation of silicon nanoinclusions [which, without dop- upon the transition. The probability of radiative holeÐ ing, would remain in the amorphous (nonluminescent) electron recombination occurring without the participa- state] into the crystalline (luminescent) state. tion of phonons appears to be proportional to the ratio (vi) Impurity atoms can also affect the formation of (a/r)8 [7] (where a is the lattice parameter and r is the silicon nanocrystals in a different way [4]. In particular, size of the nanocrystal) and remains very small (102Ð the precipitates formed by impurity atoms during 104 sÐ1) for typical sizes of quantum dots (3Ð5 nm). In annealing can serve as centers of heterogeneous nucle- this case, according to our estimates, the introduction of ation of silicon nanoinclusions. In the process, the num- donor atoms does not lead to an appreciable increase in ber of silicon nanocrystals should increase and, hence, the recombination probability. The analysis showed their mean size should decrease. This should result in that the phonon-assisted transitions occur with a sub- an enhancement of the photoluminescence, provided stantially higher probability. In the situation where the the silicon nanocrystals are not too small in size. How-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

THE INFLUENCE OF P+, B+, AND N+ ION IMPLANTATION 19 ever, if the excess of silicon in the matrix is insufﬁcient, part of the silicon nanocrystals will be so small in size that they cannot be involved in an ensemble of silicon inclusions as luminescence centers in this spectral range and, consequently, the photoluminescence will be weakened.

3. SAMPLES AND EXPERIMENTAL TECHNIQUE PL intensity, arb. units For ion implantation, we used 0.3- to 0.6-µm-thick SiO films thermally grown on a silicon substrate. The 2 0123 + implantation of Si ions was performed at an ion energy + 17 –2 Φ P dose, 10 cm E = 140 keV. The dose of implanted ions Si was equal 17 Ð2 to 1 × 10 cm . After the ion implantation, the samples Fig. 1. Dependence of the PL intensity on the dose of were annealed in a dried nitrogen stream at tempera- implanted phosphorus ions for the SiO2:nc-Si system pre- tures of 1000 and 1100°C for 2 h. The films with silicon pared at 1000°C. The dashed line indicates the initial PL nanocrystals thus prepared and the films not subjected intensity. to annealing after the silicon ion implantation were doped through implantation with phosphorus, boron, and nitrogen ions under the following conditions: E = Φ × 16 Ð2 + 150 keV and P = 1 10 cm for P ions, E = 60 keV Φ × 16 Ð2 + Si 2s P 2p and B = (0.1Ð10) 10 cm for B ions, and E = 70 keV and Φ = (0.1Ð100) × 1015 cmÐ2 for N+ ions. (Si–O) N (Si) (Si–P) (P) (P–Si) The ion energies were chosen in such a way as to provide penetration of the ions throughout the thickness of the film. The density of the ionic current in the course of implantation was no higher than 3 µA/cm2; therefore, the increase in sample temperature did not exceed several tens of degrees. After the ion implantation, the Intensity, arb. units samples were annealed at a temperature of 1000 or ° 1100 C for 2 h. The photoluminescence spectra were 165 160 150 140 130 120 measured in the wavelength range 700Ð1100 nm upon Binding energy, eV excitation with an Ar laser (λ = 488 nm). The state of the chemical elements was investigated using x-ray photoelectron spectroscopy on an ESCALAB MKZ Fig. 2. X-ray photoelectron spectrum of the SiO2:nc-Si sys- ° (VG) spectrometer (monochromated AlKα radiation). tem prepared at 1100 C, doped with phosphorus, and then annealed at 1100°C. The Ag 3d5/2 peak was recorded with a spectrometer resolution of 1.0 eV. Prior to recording the x-ray photoelectron spectra, the samples were etched with an Ar+ photoluminescence. In [7, 16], the SiO2:nc-Si system ion beam (8 keV) until the C 1s line associated with prepared at 1100°C was doped with phosphorus ions accidental carbon contaminations of the surface disap- followed by successive isochronal annealings at pro- peared. gressively higher temperatures. It seems likely that, in this case, the preparation conditions are favorable for 4. RESULTS AND DISCUSSION precipitating phosphorus from a supersaturated solid solution. The precipitation brings about an increase in In our earlier works [5, 6], we demonstrated that the phosphorus ion doping of the SiO :nc-Si system pre- the mechanical stresses and, as a consequence, the 2 breaking of bonds, i.e., the formation of nonradiative- pared through ion implantation followed by annealing at 1000°C leads to a considerable enhancement of the recombination centers. The x-ray photoelectron spectra photoluminescence. As an illustration, Fig. 1 shows the also indicate that phosphorus is incorporated into sili- dependence of the photoluminescence intensity on the con nanocrystals and can precipitate in them at high dose of implanted phosphorus ions [6]. It is assumed temperatures (Fig. 2). As is clearly seen from Fig. 2, the that the photoluminescence enhancement can occur x-ray photoelectron spectrum exhibits peaks attributed through a combination of mechanisms i, ii, and, possi- to free phosphorus and peaks associated with the phos- bly, iii. However, as was shown in [7, 16], the phospho- phorus atoms bonded to the silicon atoms. Since phos- rus ion doping of the system prepared under other phorus readily dissolves in SiO2 and forms bonds with annealing conditions can result in quenching of the oxygen atoms (phosphorosilicate glass) [2, 17], it is

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 20 TETELBAUM et al.

Without B Si+ annealing at 1000°C N+ annealing at 1000°C

1 ×20 3 PL intensity, arb. units 2 Si+ annealing at 1000°C N+ 0 700 800 900 1000 1100 annealing at 1000°C Wavelength, nm

Fig. 3. Photoluminescence spectra of the SiO2:nc-Si system prepared at 1000°C, doped with boron, and then annealed at 1000°C. Dose of B+ ions: (1) 1015, (2) 1016, and (3) 1017 cmÐ2. PL intensity, arb. units highly improbable that the phosphorus precipitates are located in the SiO2 matrix rather than in the silicon + + nanocrystals or at their interfaces. Si N annealing at 1000°C The ion-implantation doping with boron (performed under the same conditions for which phosphorus ion implantation provides an enhancement of photoluminescence) leads to photoluminescence quenching (Fig. 3). In our opinion, this phenomenon can be explained in terms of the trivalent state of boron and the large difference between the covalent radii of boron and silicon. Let us consider a pentavalent (phosphorus) atom substituting for a silicon atom located at the nc- 14 15 16 17 Si/SiO2 interface in the vicinity of the dangling bond. In 10 10 10 10 this case, the pentavalent phosphorus atom donates four N+ dose, cm–2 electrons for the formation of “normal” bonds with the nearest neighbor atoms, whereas the ﬁfth electron ter- Fig. 4. Effect of ion-implantation doping with nitrogen on minates the dangling bond. Within this interpretation, the PL intensity for the SiO2:nc-Si system prepared and the doping with Group III elements (boron) can bring doped under different conditions. The dashed line indicates about the formation of new dangling bonds. The the initial PL intensity. mechanical stresses arising in the SiO2:nc-Si system upon dissolution of an impurity atom in the lattice of silicon nanocrystals depend on the difference between sequently, the photoluminescence of large-sized nanoc- the covalent radii. The larger the difference, the stron- rystals is quenched to a greater extent as compared to ger the stresses. The ion-implantation doping with a that of small-sized nanocrystals. As a result, the maximum of the photoluminescence band is shifted toward small B+ dose leads not only to the quenching of photo- the blue spectral range. luminescence but also to a shift in the maximum of the photoluminescence band toward the short-wavelength Unlike phosphorus and boron, nitrogen poorly dis- range. This can be explained as follows. The photolu- solves in silicon and can form SixNy precipitates. Actu- minescence spectrum is a superposition of peaks corre- ally, the ion-implantation doping with nitrogen leads to sponding to nanocrystals of different sizes. The larger photoluminescence quenching (Fig. 4). It should be the crystal size, the greater the shift in the maximum of noted that, when nitrogen is introduced immediately the photoluminescence band toward the long-wave- after the silicon ion implantation, the dependence of the length range [13]. At low concentrations, the mean dis- photoluminescence intensity on the dose of implanted tance between the boron atoms is of the order of the nitrogen ions exhibits nonmonotonic behavior. Accord- nanocrystal size. It is evident that the probability of ing to Kachurin et al. [4], the nonmonotonic dose boron being incorporated into large-sized nanocrystals dependence of the photoluminescence intensity can be is higher than that into small-sized nanocrystals. Con- associated with the inﬂuence of nitrogen ions on the

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 THE INFLUENCE OF P+, B+, AND N+ ION IMPLANTATION 21 formation of nanocrystals. At certain concentration REFERENCES ratios of nitrogen and silicon, the SixNy precipitates 1. M. Fujii, S. Hayashi, and K. Yamamoto, J. Appl. Phys. serve as nucleation centers of new silicon nanocrystals 83, 7953 (1998). and, thus, bring about the enhancement of the photolu- 2. M. Fujii, A. Mimura, S. Hayashi, and K. Yamamoto, minescence. With a further increase in the nitrogen Appl. Phys. Lett. 75 (2), 184 (1999). dose (the number of silicon nanocrystals), the deﬁcit of 3. A. Mimura, M. Fujii, S. Hayashi, et al., Phys. Rev. B 62 the silicon dissolved in the SiO2 matrix and the (19), 12625 (2000). decrease in the sizes of the nanocrystals formed begin 4. G. A. Kachurin, S. G. Yanovskaya, K. S. Zhuravlev, and to manifest themselves (see mechanism vi). M.-O. Ruault, Fiz. Tekh. Poluprovodn. (St. Petersburg) 35 (10), 1235 (2001) [Semiconductors 35, 1182 (2001)]. 5. D. I. Tetelbaum, O. N. Gorshkov, S. A. Trushin, et al., 5. CONCLUSIONS Nanotechnology 11, 295 (2000). 6. D. I. Tetelbaum, S. A. Trushin, V. A. Burdov, et al., Nucl. Thus, the effect of ion-implantation doping on the Instrum. Methods Phys. Res. B 174, 123 (2001). luminescence properties of the SiO2:nc-Si system is 7. V. A. Burdov, O. N. Gorshkov, A. N. Mikhaylov, et al., governed by a number of structural and electronic fac- Izv. Akad. Nauk, Ser. Fiz. 67 (2), 186 (2003). tors. The role played by each factor depends on the type 8. G. A. Kachurin, I. E. Tischenko, K. S. Zhuravlev, et al., of implanted impurity, the impurity concentration, and Nucl. Instrum. Methods Phys. Res. B 122, 571 (1997). the heat treatment conditions. As a result, the doping 9. K. S. Min, K. V. Scheglov, C. M. Yang, et al., Appl. Phys. can lead to either enhancement or degradation of the Lett. 69, 2033 (1996). photoluminescence. In this respect, the ion-implanta- 10. B. Garrido Fernandez, M. Lopez, C. Garcia, et al., tion doping opens up fresh opportunities for investigat- J. Appl. Phys. 91 (2), 798 (2002). ing the physicochemical mechanisms of impurity 11. T. Shimizu-Iwayama, K. Fujita, S. Nakao, et al., J. Appl. effects and, in particular, for experimental veriﬁcation Phys. 75, 7779 (1994). of theoretical models. 12. Y. Kanemitsu and S. Okamato, Phys. Rev. B 58, 9652 (1998). 13. M. Lannoo, C. Delerue, and G. Allan, J. Lumin. 70, 170 ACKNOWLEDGMENTS (1996). 14. G. A. Kachurin, S. G. Yanovskaya, D. I. Tetel’baum, and We would like to thank V.K. Vasil’ev and D.L. Vaœn- A. N. Mikhaylov, Fiz. Tekh. Poluprovodn. (St. Peters- shteœn for their assistance in performing the experi- burg) 37 (6), 738 (2003) [Semiconductors 37, 713 ments and G.A. Kachurin for his participation in dis- (2003)]. cussions of the results and helpful remarks. 15. Problems in Radiation Technology of Semiconductors, This work was supported by the International Asso- Ed. by L. S. Smirnov (Nauka, Novosibirsk, 1980). ciation of Assistance for the promotion of cooperation 16. D. I. Tetelbaum, S. A. Trushin, A. N. Mikhaylov, et al., Physica E: Low-Dimens. Syst. Nanostruct. 16 (3Ð4), 410 with scientists from the New Independent States of the (2003). former Soviet Union (project INTAS no. 00-0064) and 17. J. B. Beales and C. R. Day, Phys. Chem. Glasses 21 (1), the program of the Ministry of Education of the Russian 5 (1980). Federation “Higher School Research in Priority Direc- tions of Science and Engineering” (subprogram no. 205). Translated by O. Borovik-Romanova

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 170Ð172. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 168Ð170. Original Russian Text Copyright © 2004 by Dremin, Larionov, Timofeev.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Bose Condensation of Interwell Excitons in Lateral Traps: A Phase Diagram A. A. Dremin, A. V. Larionov, and V. B. Timofeev Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia e-mail: [email protected]

Abstract—The luminescence of interwell excitons in GaAs/AlGaAs double quantum wells (nÐiÐn heterostructures) containing large-scale random-potential ﬂuctuations was studied. The study dealt with the properties of an exciton whose photoexcited electron and hole are spatially divided between the neighboring quantum wells under density variation and at temperatures of down to 0.5 K. We investigated domains ~1 µm in size, which act as macroscopic exciton traps. Once the resonance laser pump power reaches a certain threshold, a very narrow delocalized exciton line appears (with a width less than 0.3 meV), which grows strongly in intensity with increasing pump power and shifts toward lower energies (by approximately 0.5 meV) in accordance with the exciton buildup in the lowest state in the domain. As the temperature increases, this spectral line disappears in a nonactivated manner. This phenomenon is assigned to Bose condensation occurring in the quasi-two-dimensional system of interwell excitons. The critical exciton density and temperature were determined within the temperature interval studied (0.5 to 3.6 K), and a phase diagram specifying the exciton condensate region was constructed. © 2004 MAIK “Nauka/Interperiodica”.

An intense search has been under way in recent excited resonantly using tunable Ti sapphire laser years [1Ð16] to establish the existence of BoseÐEinstein pumping. exciton condensation in two-dimensional (2D) semi- When the pumping is increased (to ≥50 µW), a nar- conductor heterostructure systems. In quasi-two- row line appears abruptly at the violet edge of the wide dimensional quantum confined systems, Bose conden- band associated with localized excitons (Fig. 1). The sation can take place at finite temperatures. Spatial con- intensity of this line increases superlinearly with pump- finement in the quantum-well plane may originate from ing (see inset to Fig. 1), and the line narrows and shifts large-scale random-potential fluctuations associated by about 0.5 meV toward lower energies. The minimum with variation in the quantum-well width at heteroint- width of this line is 350 µeV for a spectrometer spectral erfaces. Excitons are easier to accumulate in systems slit width of about 200 meV. As the pumping is with lateral confinement, and the density of excitons in increased still further (above 0.5 mW), the narrow such regions may greatly exceed their average density interwell exciton line starts to broaden monotonically [13]. Therefore, the critical conditions conducive to and shift toward higher energies. Bose condensation of interwell excitons are easier to realize in lateral domains. With this purpose in mind, The line intensity I decreases with increasing tem- we studied the properties of interwell excitons under perature with only a small variation of the linewidth, variation of their density and temperature in until at T = 3.6 K this line disappears against the struc- GaAs/AlGaAs double quantum wells with large- tureless background of the localized-exciton spectrum, scale random-potential fluctuations produced by the which retains its shape (Fig. 2). It is essential that the MBE growth interruption technique at quantum-well decrease in the line intensity I with increasing temper- walls [17]. ature does not have an activated character. By measuring the temperature dependence of the line intensity I at A metal mask (an aluminum film) 100 nm thick was different pumping levels, we established the following deposited on the surface of an nÐiÐn structure with the temperature behavior: I ∝ [1 Ð (T/T )α], where I is the architecture described in [9]. Circular holes with a min- T C T imum size of down to 0.5 µm were etched in this film line intensity at temperature T, TC is the critical temperature at which this line disappears in the spectrum at a by using electron beam lithography. The luminescence α ≤ signals were excited and detected through holes pre- given fixed excitation, and 1.5. pared in this manner. Results indicating exciton con- The observed phenomenon exhibits all features typ- densation were obtained with a sample pumped opti- ical of a phase transition associated with the Bose con- cally through windows less than 1 µm in diameter. The densation of excitons; namely, a new, collective exciton heavy-hole interwell excitons (1s HH excitons) were phase forms as a critical density and a critical tempera-

BOSE CONDENSATION OF INTERWELL EXCITONS IN LATERAL TRAPS 171

1.0

0.5 I Intensity, arb. units

0 0 50 150 250 P, µW 250

Intensity Intensity 200

150 250 200 120 150 100 120 100 70 70 50 50 1.530 1.535 1.540 1.530 1.535 1.540 Energy, eV Energy, eV

Fig. 1. Photoluminescence spectra of interwell excitons, Iex, measured at different direct-exciton resonant excitation power levels. The numbers next to the spectra identify the pump power in µW. The spectra shown on the right were obtained by subtracting the structureless continuum under the line. T = 1.51 K.

1.0

I I 0.5 Intensity, arb. units

1.5 2.0 2.5 0 T, ä 1.8

Intensity 1.8 Intensity 2.1

2.1

2.4 2.4

2.7 2.7

1.530 1.535 1.540 1.530 1.535 1.540 Energy, eV Energy, eV Fig. 2. Temperature dependence of the intensity of the narrow photoluminescence line obtained at a pump power of 150 µW. The numbers next to the spectra are temperatures measured in kelvins. The spectra shown on the right were obtained by subtracting the structureless continuum under the line.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

172 DREMIN et al.

300 ACKNOWLEDGMENTS 200 This study was supported by the Russian Founda- 250 100 tion for Basic Research and the State research and development program on nanostructures. 60 200 [arb. units] 40 P

log 20 REFERENCES 150 0.4 0.6 1 2 4 log(T, K) 1. Yu. E. Lozovik and V. I. Yudson, Pis’ma Zh. Éksp. Teor. , arb. units 3/2 P P ~ I ~ N ~ T Fiz. 22, 556 (1975) [JETP Lett. 22, 274 (1975)]. 100 Bose condensate C C C region 2. T. Fukuzawa, E. E. Mendez, and J. M. Hong, Phys. Rev. 50 Ti–Sa Lett. 64, 3066 (1990). He–Ne 3. L. V. Butov, A. Zrenner, G. A. Abstreiter, et al., Phys. 0 Rev. Lett. 73, 304 (1994); L. V. Butov, in Proceedings of 0.5 1.5 2.5 3.5 4.0 the 23rd International Conference on Physics of Semi- T, K conductors, Berlin (1996). 4. V. B. Timofeev, A. V. Larionov, A. S. Ioselevich, et al., Pis’ma Zh. Éksp. Teor. Fiz. 67, 580 (1998) [JETP Lett. Fig. 3. Phase diagram of the Bose condensate of interwell excitons obtained in the temperature interval 0.5Ð3.6 K. 67, 613 (1998)]. 5. V. V. Krivolapchuk, E. S. Moskalenko, A. L. Zhmodikov, et al., Solid State Commun. 111, 49 (1999). ture are reached. We attempted to establish a phase dia- 6. L. V. Butov, A. Imamoglu, A. V. Mintsev, et al., Phys. gram including the region of the Bose condensate of Rev. B 59, 1625 (1999). interwell excitons. To do this, we studied the depen- 7. A. V. Larionov, V. B. Timofeev, J. M. Hvam, et al., JETP 90, 1093 (2000). dence of the photoluminescence spectra on pump 8. L. V. Butov, A. V. Mintsev, Yu. E. Lozovik, et al., Phys. power at ﬁxed values of temperature in the interval 0.5Ð Rev. B 62, 1548 (2000). 3.6 K and determined the threshold power PC at which 9. A. V. Larionov, V. B. Timofeev, J. M. Hvam, et al., the narrow line appears (or disappears) in the spectrum. Pis’ma Zh. Éksp. Teor. Fiz. 75, 233 (2002) [JETP Lett. The phase diagram was constructed in the P ÐT coor- 75, 200 (2002)]. C 10. L. V. Butov, C. W. Lai, A. L. Ivanov, et al., Nature 417, dinates in the region within which the intensity of the 47 (2002). narrow line depends linearly on the pump power. The 11. L. V. Butov, A. C. Gossard, and D. S. Chemla, Nature phase diagram thus obtained is presented in Fig. 3 in 418, 751 (2002). both a linear and a logÐlog scale. 12. D. Yoshioka and A. H. MacDonald, J. Phys. Soc. Jpn. 59, 4211 (1990); X. M. Chen and J. J. Quinn, Phys. Rev. The Bose condensation is observed to occur within Lett. 67, 895 (1991). a limited interval of exciton concentrations, Nloc < Nex < 13. Xuejun Zhu, P. L. Littlewood, M. S. Hybersten, and T. Rice, Phys. Rev. Lett. 74, 1633 (1995). NIÐM. The lower limit is due to the strong exciton localization at defects. We estimated the density of localized 14. J. Fernandez-Rossier and C. Tejedor, Phys. Rev. Lett. 78, 4809 (1997). ≤ × 9 Ð2 states in our structures as Nloc 3 10 cm . It is the 15. Yu. E. Lozovik and O. L. Berman, Zh. Éksp. Teor. Fiz. localized states that account for the unusual shape of 111, 1879 (1997) [JETP 84, 1027 (1997)]. the phase diagram at low temperatures. The upper 16. Yu. E. Lozovik and I. V. Ovchinnikov, Pis’ma Zh. Éksp. bound is related to the excitons breaking down at the Teor. Fiz. 74, 318 (2001) [JETP Lett. 74, 288 (2001)]. insulatorÐmetal transition, N ≤ 1011 cmÐ2. This den- 17. S. W. Brown, T. A. Kennedy, D. Gammon, et al., Phys. IÐM Rev. B 54, R17339 (1996). sity corresponds to a dimensionless parameter rS = π ≤ 1/NIÐMaB 2. Translated by G. Skrebtsov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 173Ð175. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 171Ð173. Original Russian Text Copyright © 2004 by Bagaev, Vodop’yanov, Vinogradov, Zaœtsev, Kozyrev, Mel’nik, Onishchenko, Karczewski. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Electronic States and Vibration Spectra of CdTe/ZnTe Quantum Dot Superlattices V. S. Bagaev*, L. K. Vodop’yanov*, V. S. Vinogradov*, V. V. Zaœtsev*, S. P. Kozyrev*, N. N. Mel’nik*, E. E. Onishchenko*, and G. Karczewski** *Lebedev Physical Institute, Russian Academy of Sciences, Leninskiœ pr. 53, Moscow, 119991 Russia e-mail: [email protected] **Institute of Physics, Polish Academy of Sciences, Warsaw, 02-668 Poland

Abstract—Electronic and vibrational states in CdTe/ZnTe quantum dot superlattices are studied using optical spectroscopy techniques (photoluminescence in a wide temperature range, IR reflection, and Raman scattering). The effect of the ZnTe barrier layer thickness on the luminescence spectra of the structures is discussed. The luminescence from electronically coupled islands is assumed to be due to spatially indirect excitons because of the specific features of the CdTe/ZnTe heterostructure band structure. A combination of quantum- dot vibrational modes, which has not been observed earlier, is detected in the Raman spectra. Analysis of the lattice IR reflection spectra shows that, in the case of large barrier thicknesses between the quantum-dot planes, elastic stresses are concentrated in the Zn1 Ð xCdxTe layers, whereas in structures with lower barrier thicknesses the elastic-strain distribution exhibits a more complicated pattern. © 2004 MAIK “Nauka/Interperiodica”.

1. Structures with multiple quantum-dot (QD) to the selection rules, Raman scattering only by optical planes, which are sometimes called quantum dot super- phonons is allowed in this conﬁguration. lattices (QDSLs), were grown by molecular-beam epitaxy on GaAs (100) substrates. First, a CdTe buffer layer 2. Figure 1 shows luminescence spectra of QDSLs 4.5 µm thick was deposited on a substrate and then a with ZnTe barrier layers 12, 25, and 75 MLs thick QDSL consisting of 200 CdTe layers 2.5 monolayers (samples B12, B25, B75, respectively) recorded at 5 K. (MLs) thick each was grown on it, with the layers sep- The luminescence spectrum of sample B75 is virtually arated from each other by ZnTe barriers with a thick- identical to those from structures with single ness varying from 12 to 75 MLs. The grown structures CdTe/ZnTe QD planes and with a comparable nominal were examined with a JEOL 2000EX transmission CdTe layer thickness (see, e.g., [2]). However, the situ- electron microscope with a resolution of 0.27 nm. ation becomes radically different as the CdTe barrier Analysis of the lattice parameters, which varied along layer thickness is decreased. For a barrier layer thick- the growth direction, showed that each of the QDs was ness equal to 25 MLs, the luminescence line is consid- a layer of the Zn1 Ð xCdxTe solid solution in which there erably (more than two times) narrower than in the case were regions (islands) 2 nm thick and 6Ð10 nm in diameter (QDs) enriched in cadmium. It was found that, in the case of ZnTe barrier layers less than 25 MLs B12 B75 B25 thick, the QDs in adjacent layers were correlated in position [1]. Photoluminescence spectra were excited by an HeÐ Cd laser (wavelength 4416 Å) and recorded in the temperature range 5Ð150 K. A DFS-24 double-pass monochromator with a limiting resolution better than 0.1 Å was used to analyze the spectra. The lattice IR reﬂec- tion spectra at 300 K were recorded on a Bruker IFS-55 Fourier spectrometer with a spectral resolution higher PL intensity, arb. units than 1 cmÐ1. Raman spectra were excited with different 2+ Ar -laser lines and measured with an U-1000 spec- 2.12 2.162.202.24 2.28 2.32 trometer in the back scattering geometry (spectral reso- Energy, eV lution 1 cmÐ1). The scattered light was analyzed along the direction of structure growth (z axis) for the sample Fig. 1. Photoluminescence spectra taken from QD superlat- orientation x || [100], y || [010], and z || [001]. According tices with ZnTe barrier layers 12, 25, and 75 MLs thick.

174 BAGAEV et al. sion was due to direct excitons, whereas on the whole the light emission from the structure was associated with indirect excitons. A potential well that is produced for a hole by elas- B75 tic strains and Coulomb interaction with an electron (for which a fairly deep potential well arises in a B25 Zn1 − xCdxTe layer for the Zn1 − xCdxTe/ZnTe structures) is rather shallow, and the characteristic radiative recombination time of an indirect exciton significantly B12 Intensity, arb. units exceeds that of a direct exciton. Due to both these factors, the luminescence from electronically coupled islands will be quenched fairly rapidly with increasing 100 140180 220 temperature. The temperature dependences of Wave number, cm–1 CdTe/ZnTe QD superlattice luminescence will be analyzed in detail in a future publication. Fig. 2. Raman spectra of samples B12, B25, and B75. For the sake of pictorial convenience, the spectra are shifted 3. Due to the formation of QDs, both the electronic along the ordinate axis. and phonon spectra are rearranged, which manifests itself in the Raman scattering spectra. Figure 2 shows Raman spectra of samples B12, B25, and B75 excited of isolated layers. This effect is likely due to a by the 4880-Å line. As an example, let us discuss the decreased spread in the QD sizes formed during the spectrum of the QDSL with a barrier thickness of growth of structures with a large number of QD layers 25 MLs. There are three bands in this Raman spectrum. and was first observed for SiGe/Si QD superlattices [3]. The high-frequency band at 201 cmÐ1 corresponds to As the barrier thickness is decreased to 12 MLs, an the ZnTe LO phonon mode, whose frequency is 2 cmÐ1 additional band appears in the luminescence spectrum. lower than that in the bulk ZnTe. The other two bands This band is due to excitons localized on correlated lie in the range of vibrational CdTe excitations. The islands in adjacent QD planes. band corresponding to the CdTe LO phonon mode at The activation energy for luminescence quenching 171 cmÐ1 is missing from the Raman spectrum. The was determined from the temperature dependence of mode observed at 139 cmÐ1 is close to the CdTe TO the integrated QDSL luminescence intensity. As the phonon mode (140 cmÐ1) but is Raman-active. The ZnTe barrier layer thickness is decreased, this energy strong low-frequency band at 126 cmÐ1 is not typical of decreases from more than 60 meV for sample B75 to IIÐVI compounds. We note that the observed Raman less than 30 meV for sample B12. The temperature spectrum is resonant in character. Indeed, the Raman dependences of the QDSL luminescence exhibit a very spectrum obtained from the same 25-MLs sample interesting property: as the temperature is increased, under excitation with the 5145-Å line exhibits the main the luminescence is quenched more rapidly in the case features of the spectrum excited with the 4880-Å line of electronically coupled islands. In sample B12, as the but has a much lower intensity. By comparing the temperature is increased to 80 K, only the line from iso- Raman spectra of different samples, it can be seen that lated Zn1 Ð xCdxTe islands survives in the luminescence all observed bands shift toward lower energies with spectrum. This property is surprising at first glance increasing ZnTe barrier layer thickness. This effect is (because the energy level for coupled islands is deeper due to a decrease in the lattice parameter averaged over than that for isolated ones) and is likely due to specific the sample volume. features of the Zn1 Ð xCdxTe/ZnTe heterostructure band The experimental data obtained are analyzed in structure. For this heterostructure, the valence band off- detail in [5]; here, we will dwell only on the main con- set is almost entirely caused by the strains due to the clusions. The vibrational modes with frequencies near difference in lattice parameters between the two mate- 140 and 120 cmÐ1 may be identified with the symmetric rials. In structures with small distances between QD Coulomb (interface) QD mode and with the symmetric layers, spatially indirect excitons can form because of phonon mode confined in a QD, respectively. This the strains in the ZnTe barrier layer (see Section 3). We mode combination has not been observed earlier in QD believe that such a situation occurs in the case of elec- structures. tronically coupled islands, because it is in the region between two CdTe QDs that the strains in the ZnTe bar- The presence of a thick CdTe buffer layer hampers rier layer are maximal and can cause a potential well for the observation of vibrational excitations in QDs in IR a light hole to arise in this region. A situation similar in reflection spectra. However, these spectra can provide certain respects was observed in GaAs/AlAs superlat- information on elastic strains in the structures under tices [4], where local changes in the thickness of GaAs study. Figure 3 shows the reflection spectra of samples and AlAs layers caused a change in the structure type; B12 and B25. The reflection band near 270 cmÐ1 is the namely, in regions with thicker GaAs layers, light emis- reststrahlen band of the GaAs substrate, and the fea-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

ELECTRONIC STATES AND VIBRATION SPECTRA 175 tures observed in the spectra near 140 and 170 cmÐ1 correspond to CdTe and ZnTe vibrational modes in the 1.0 buffer layers and QDSL. The mathematical treatment of the experimental 0.8 spectra was performed using an analysis of the variance in terms of a model structure consisting of a thin film (a 0.6 QDSL and a buffer layer) deposited on a semi-infinite substrate. The calculated GaAs lattice mode frequency 0.4 for a substrate with a CdTe buffer layer 4.5 µm thick Reflection deposited on it is 267 cmÐ1, which is 3 cmÐ1 less than the lattice mode frequency of the bulk GaAs crystal, and 0.2 the decay constant γ for this mode is calculated to be 8 cmÐ1. 0 140 180 220 260 300 The following very interesting effect was detected Wave number, cm–1 in studying the dependence of the ZnTe vibrational mode on the barrier layer thickness. On the basis of Fig. 3. Lattice IR reflection spectra for samples B12 and analyzing the variance, it was established that in sample B25. The experimental data are represented by squares for B12, in which the barrier layer is the thinnest (12 MLs), B12 and by circles for B25. Solid lines are the calculated ZnTe vibrations are represented by a single strong spectra. For pictorial convenience, the spectrum taken from ω Ð1 sample B25 is shifted by 0.2 along the ordinate axis. mode at t1 = 172 cm . In sample B25, the frequency ω Ð1 of the strong mode increases to t1 = 173.5 cm and an ω Ð1 additional mode appears at t2 = 169 cm . In sample detected a combination of QD vibrational modes that B75 (not represented in Fig. 3), in which the ZnTe bar- has not been observed earlier. rier layers separating Zn1 Ð xCdxTe layers are 75 MLs thick, ZnTe vibrations are represented by two modes, at ACKNOWLEDGMENTS ω Ð1 ω Ð1 t1 = 176 cm and t2 = 165 cm , and their oscillator strengths are comparable in magnitude. This study was supported by the Russian Founda- tion for Basic Research (project nos. 03-02-16854, 03- As the barrier layer thickness is varied, the strong- 02-17110) and the Russian Academy of Sciences Com- ω Ð1 mode frequency t1 varies from 172 to 176 cm and, mittee for support of young scientists. within the limits of experimental error, reaches the ω Ð1 transverse-mode frequency t = 177 cm of pure ZnTe. Therefore, in sample B12, the thin ZnTe barrier layers REFERENCES are highly stretched by the adjacent Zn1 Ð xCdxTe layers 1. S. Mackowski, G. Karczewski, T. Wojtowicz, et al., and by the thick CdTe buffer layer. In sample B75, the Appl. Phys. Lett. 78, 3884 (2001). barrier layers are sufficiently thick for the elastic 2. V. V. Zaœtsev, V. S. Bagaev, and E. E. Onishchenko, Fiz. stresses to relax in them. Tverd. Tela (St. Petersburg) 41, 717 (1999) [Phys. Solid 4. Thus, we have investigated the temperature State 41, 647 (1999)]. dependences of the luminescence spectra of 3. J. Tersoff, C. Teichert, and M. G. Lagally, Phys. Rev. CdTe/ZnTe QD superlattices. The light emission from Lett. 76, 1675 (1996). electronically coupled CdTe islands was proposed to be 4. D. Luerssen, A. Oehler, R. Bleher, and H. Kalt, Phys. due to spatially indirect excitons. It has been estab- Rev. B 59, 15862 (1999). lished that, in structures with thick ZnTe barrier layers 5. L. K. Vodop’yanov, V. S. Vinogradov, N. N. Mel’nik, and separating QD planes, elastic strains are concentrated G. Karczewski, Pis’ma Zh. Éksp. Teor. Fiz. 77, 171 (2003) [JETP Lett. 77, 143 (2003)]. in Zn1 Ð xCdxTe layers, whereas in structures with thinner barrier layers the elastic-strain distribution exhibits a more complicated pattern. In Raman spectra, we Translated by Yu. Epifanov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 176Ð178. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 174Ð176. Original Russian Text Copyright © 2004 by Valakh, Strelchuk, Semenova, Sadofyev.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Resonant Stokes and Anti-Stokes Raman Scattering of Light in CdSe/ZnSe Nanostructures M. Ya. Valakh*, V. V. Strelchuk*, G. N. Semenova*, and Yu. G. Sadofyev** * Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, pr. Nauki 45, Kyiv, 03028 Ukraine ** Lebedev Physical Institute, Russian Academy of Sciences, Leninskiœ pr. 53, Moscow, 117927 Russia e-mail: [email protected]

Abstract—Raman scattering spectra of CdSe/ZnSe multilayer nanostructures with a CdSe insert of a nominal thickness of 2.1 monolayers were studied. A heavy dependence of the intensity and of the frequency position of the multiphonon Stokes and anti-Stokes LO bands on the exciting photon energy was detected. The results obtained are interpreted as a resonance with various exciton transitions in the CdSe insert and barrier ZnSe layers. A difference between the Stokes and anti-Stokes frequencies of LO bands observed as the resonance conditions are varied conﬁrms the inhomogeneous nature of the photoluminescence band of CdSe quantum dots. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION by ZnSe barrier layers. The thickness of a barrier layer Semiconductor quantum dots (QDs) based on wide- was 18 nm, and the thicknesses of the buffer and cap band-gap IIÐVI compounds are a promising material ZnSe layers were 200 and 100 nm, respectively. The for the development of efficient light-emitting opto- buffer ZnSe and barrier ZnSe layers were grown at 280 and 230°C, respectively. The CdSe layers were depos- electronic devices. The driving force of the QD self- ° assembling process is the elastic stress fields arising ited at 230 C. To initiate the formation of 3D CdSe islands, heating to 340°C was used, followed by cool- due to the difference between the substrate and hetero- ° layer lattice constants. The formation of three-dimen- ing to 230 C in selenium vapor. The transition from the sional (3D) coherently strained QDs causes a decrease 2D deposited CdSe layer to the formation of 3D struc- in the elastic energy of the system. Nanometer-sized tures was monitored in situ by using a high-energy elec- (10Ð100 nm) CdSe QDs were grown by molecular- tron diffractometer. beam epitaxy (MBE). In contrast, e.g., to the case of The RS and PL spectra were measured in the reflec- InAs/GaAs heterostructures, CdSe layer deposition is tion geometry by using a DFS-24 double spectrometer. accompanied by active interdiffusion and segregation The spectra were excited by discrete emission lines of an of Cd atoms at CdSe/ZnSe heterointerfaces. These pro- Ar+ laser. The RS spectral resolution was 1Ð2 cmÐ1. The cesses are caused by a high nonequilibrium density of frequency position of a spectral line was determined with cation vacancies forming during the epitaxial growth. an accuracy better than 0.2 cmÐ1 due to simultaneous As a result, a 10-MLs-thick two-dimensional (2D) measurement of laser plasma lines in the spectrum. layer of mixed Zn1 Ð xCdxSe composition is formed in the ZnSe host during deposition of a CdSe epitaxial layer with a nominal thickness of 0.5Ð3.0 monolayers 3. RESULTS AND DISCUSSION (MLs). This layer contains nanoislands enriched with Figure 1 shows the PL spectra of a multilayer Cd. An increase in the thickness of the deposited CdSe CdSe/ZnSe structure with a nominal thickness of the layer causes an increase in the Cd concentration in the CdSe insert of 2.1 MLs observed under resonant exci- 2D layer and islands [1]. tation in the region of intrinsic absorption of ZnSe lay- This study is devoted to Stokes and anti-Stokes Raman ers (Fig. 1a) and in the region of the emission band of scattering (RS) of light and photoluminescence (PL) CdSe QDs (Fig. 1b). The spectra contain an intense excited nonresonantly in both ZnSe layers and CdSe QDs. asymmetric band of the CdSe QD emission at 2.559 eV (Fig. 1a) and 2.554 eV (Fig. 1b). The band has a structure on its high-energy slope at room temperature and 2. EXPERIMENTAL on its low-energy slope at a low temperature. The band CdSe/ZnSe structures were grown by MBE on asymmetry is interpreted as being due to the simulta- semi-insulating GaAs(100). The samples contained neous contribution to PL coming from the 2D wetting either a single CdSe insert with a nominal thickness of Zn1 Ð xCdxSe layer (regions with a lowered Cd content 3.5 MLs or twelve CdSe layers 2.1 MLs thick separated contributing to the high-energy wing) and from CdSe

RESONANT STOKES AND ANTI-STOKES RAMAN SCATTERING OF LIGHT 177

QDs (the low-energy wing) [2]. At an excitation energy Anti-Stokes Stokes E = 2.71 eV, the resonant first- and second-order RS lines are observed against the background of band-to- 2LO (a) band PL of the ZnSe layers. At E = 2.54 eV, the reso- (ZnSe) nant RS spectrum is observed in both the Stokes and LO anti-Stokes regions. (ZnSe) × We can see from Fig. 1 that the anti-Stokes PL band 10 (Fig. 1b) is insignificantly shifted to low energies in comparison with the Stokes band (Fig. 1a) and is narrower (by 4Ð6 meV in half-width). The excitation mechanism of the CdSe QD anti-Stokes PL at low tempera- –LO (b) tures is interpreted as two-step absorption through the levels of vacancy-type defects localized at the QD inter- Intensity, arb. units × face [3]. Under resonant excitation, two-step absorption 10 through the QD energy levels also significantly contributes to anti-Stokes PL excitation in the QD absorption ZnSe-barrier –2LO LO region [4]. At elevated temperatures, thermal excitation 2LO of carriers from low- into high-energy ground states of various QDs also becomes appreciable. 2.70 2.60 2.50 2.45 Energy, eV A number of features of the spectrum in Fig. 1 are worth noting. First, this spectrum virtually continuously extends in energy from the ZnSe layer absorption Fig. 1. PL spectra of the CdSe/ZnSe nanostructure with twelve CdSe inserts of a nominal thickness of 2.1 MLs for edge to the peak of the CdSe QD emission band, which E equal to (a) 2.71 and (b) 2.54 eV; T = 300 K. may be indicative of significant fluctuations in the exc Zn1 − xCdxSe solid-solution composition of the 2D insert layer and in the sizes of small CdSe QDs. Sec- ond, the ZnSe layer PL is observed for both Stokes and Anti-Stokes Stokes anti-Stokes PL excitation modes. The anti-Stokes PL is LO(ZnSe) induced by a significant number of hot photoexcited (a) carriers generated due to two-step absorption through the QD and defect levels. Due to intrasubband relaxation of photoexcited electronÐhole pairs, nonequilib- 2LO(ZnSe) = 2.71 eV

rium LO phonons can be generated. exc Figure 2 shows the Stokes and anti-Stokes RS spec- E tra of the CdSe/ZnSe multilayer structure observed under resonant excitation in the ZnSe layer absorption –LO(ZnSe) band (Fig. 2a) and in the transparent region of all the –2LO(ZnSe) heterostructure layers (Fig. 2b). Low excitation energy densities (less than 10 W/cm2) were used in both –450 –150 0 150 450 –1 regions. Analysis of the RS spectra excited in the ZnSe Raman shift, cm absorption region is complicated by the fact that in this Anti-Stokes Stokes region the resonant RS cross section and the absorption (b) coefﬁcient, which deﬁnes the light penetration depth LO(ZnSe) into the sample, vary rapidly with frequency. The situ- Intensity, arb. units ation is also complicated by the difference in the reso- –LO(ZnSe) nance properties of the Stokes and anti-Stokes RS components. The anti-Stokes RS intensity is highest when LO(GaAs) = 2.41 eV the exciton transition frequency (i.e., the position of the TO(ZnSe) exc E PL peak in our case) coincides with the exciting light –LO(GaAs) frequency (input resonance) and is low under the con- –TO(GaAs) ditions of resonance with scattered light (output reso- TO(GaAs) nance) [5]. On the contrary, for the Stokes RS compo- –300 –100 0 100 300 nent, the LO-phonon RS intensity is higher in the case –1 of the output resonance. Thus, for anti-Stokes RS, in Raman shift, cm contrast to the resonant Stokes RS, the resonance with exciting light dominates. Hence, the intensities of the Fig. 2. RS spectrum of the multilayer CdSe/ZnSe nano- “Stokes” and “anti-Stokes” signals should be compared structure with a CdSe insert of a nominal thickness of taking this fact into account. In the case under consid- 2.1 MLs for Eexc equal to (a) 2.71 and (b) 2.41 eV; T = 300 K.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

178 VALAKH et al.

292.4 cmÐ1) and the weak TO phonon line (ν ≈ 269 cmÐ1) –LO of the GaAs substrate. The corresponding phonon lines of ZnSe and GaAs are also observed in the anti-Stokes region, but they have a lower intensity. –2LO The difference between the resonance dependences of the Stokes (IS) and anti-Stokes (IAS) RS components can be seen from Fig. 3. As the excitation photon energy is varied within the QD emission band from the high- to the low-energy wing (curves 1Ð3), the intensity ratio IS/IAS decreases. Moreover, an appreciable shift of the PL band peak to lower energies is observed when the low-energy band wing is excited (curve 3). LO(ZnSe) We compared the frequencies of the Stokes and anti- LO(GaAs) Stokes LO-and 2LO-phonon RS bands for various exci- –LO tation conditions with respect to the PL band peak. The difference between these frequencies, which is particu- 3 larly noticeable for 2LO and Ð2LO bands, indicates res- –2LO LO = 2.497 eV onant RS with various radiative electron transitions, LO exc Intensity, arb. units E 2LO which are responsible for the inhomogeneous broadening of the QD emission band associated with ﬂuctua-

2 = 2.54 eV tions in the QD sizes and, particularly, in the Cd content. exc E 2LO 4. CONCLUSIONS Thus, we have studied the resonance dependence of the Stokes and anti-Stokes RS spectra excited near the –LO CdSe QD exciton transitions. It was shown that the anti-Stokes LO-phonon RS intensity increases due to

1 = 2.6 eV the input resonance with QD electron transitions and to

exc nonequilibrium LO phonons generated in intrasubband E relaxation of photoexcited electronÐhole pairs. The fact 2.65 2.60 2.55 2.50 2.45 that the 2LO- and Ð2LO-band frequencies vary with the Energy, eV resonance conditions conﬁrms the inhomogeneous Fig. 3. Resonant RS spectra of the multilayer CdSe/ZnSe nature of the PL band. structure at various excitation photon energies. T = 300 K. ACKNOWLEDGMENTS eration (Fig. 2a), the Stokes RS conditions are closer to This study was supported by the joint RussianÐ the output resonance with ZnSe PL. Hence, the Stokes Ukrainian program “Nanophysics.” LO(ZnSe) and 2LO(ZnSe) RS line intensities are much higher than the intensities of the corresponding anti- Stokes LO-phonon RS lines, whose strengthening is REFERENCES associated with the input resonance conditions. It is 1. N. Peranio, A. Rosenauer, D. Gerthsen, et al., Phys. Rev. interesting to note that, although the Stokes and anti- B 61, 16015 (2000); D. Litvinov, A. Rosenauer, D. Ger- Stokes LO phonon RS lines are characterized by almost thsen, and N. N. Ledentsov, Phys. Rev. B 61, 16819 identical half-widths, their appreciable broadening (Γ = (2000). Ð1 10Ð11 cm ) seems to be indicative of the presence of 2. C. S. Kim, M. Kim, S. Lee, et al., J. Cryst. Growth 214Ð structural defects and of a nonuniform strain distribu- 215, 761 (2000). tion in probed ZnSe layers. 3. M. Ya. Valakh, Yu. G. Sadofyev, N. O. Korsunska, et al., Figure 2b shows the Stokes and anti-Stokes RS Semicond. Phys. Quantum Electron. Optoelectron. 5 (3), spectrum of this structure under nonresonant excitation 254 (2002). by photons with an energy of 2.41 eV, which is smaller 4. M. Ya. Valakh, N. O. Korsunska, Yu. G. Sadofyev, et al., Mater. Sci. Eng. B (2003) (in press). than the energy gap Eg of ZnSe layers (2.69 eV) and less than the energy corresponding to the QD exciton 5. A. A. Klochikhin, A. G. Plyukhin, L. G. Suslina, and E. B. Shadrin, Fiz. Tverd. Tela (Leningrad) 18 (7), 1909 emission band peak (2.554 eV). It can be seen that, in (1976) [Sov. Phys. Solid State 18, 1112 (1976)]. addition to the LO- and TO-phonon RS lines (ν ≈ 206.4 cmÐ1) of the barrier ZnSe layers, the Stokes RS spectrum contains the strong LO-phonon line (ν ≈ Translated by A. Kazantsev

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 179Ð187. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 177Ð184. Original Russian Text Copyright © 2004 by Rushchanskiœ. SEMICONDUCTORS AND DIELECTRICS

The Influence of Hydrostatic Pressure on the Static and Dynamic Properties of an InSe Crystal: A First-Principles Study K. Z. Rushchanskiœ Institute of Solid-State Physics and Chemistry, Uzhgorod National University, ul. Podgornaya 46, Uzhgorod, 88000 Ukraine e-mail: [email protected] Received December 18, 2002; in ﬁnal form, March 27, 2003

Abstract—The pressure dependences of the crystallographic parameters of the γ-InSe structure in the range up to 15 GPa are theoretically investigated using the density-functional method. It is established that, in the range from 7 to 11 GPa, the pressure dependences of the lattice parameters exhibit an anomalous behavior: the rigidity of the lattice increases in the direction of the weak bond and decreases in the plane of the layers. The layer thickness is characterized by a nonmonotonic pressure dependence. The numerical values of the lattice parameters of the crystal structure under compression are determined, and the pressure dependences of the vibrational frequencies at the center of the Brillouin zone are calculated theoretically. The results of the theoretical calculations are in good agreement with the available experimental data. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION insight into the electronic properties of layered semiconductors, because the use of external pressure opens Indium chalcogenide compounds have attracted up new possibilities for controlling the anisotropy of considerable research attention over the latter half of chemical bonding. A great body of data available in the the 20th century due to their interesting physical prop- literature on the pressure dependences of the optical erties and specific chemical structure. An increase in and kinetic properties of indium chalcogenides is due the indium content in chalcogenides In2X3 InX to the fact that these properties are governed primarily In4X3 (X = Se, Te) leads to a lowering of the symmetry by the electronic subsystem of the material. Since the and complication of the chemical bonding, which man- electronic structure of the studied objects is character- ifests itself, first, in the transformation of indium cat- ized by a van der Waals gap, the intralayer and inter- ions from the trivalent state (in In2X3) into a mixed- layer interactions manifest themselves under pressure valence state and, second, in an increase in the strength in radically different ways. After reaching a certain of InÐIn bonds [1]. Among the indium chalcogenides, pressure, these differences become less pronounced the InSe compound has been studied most extensively. (the so-called trimerization of the properties of a lay- Increased interest in these materials has been associ- ered crystal [18]). ated with their potential use in nonlinear optics [2, 3], Recent investigations have provided comprehen- solar-energy converters [4], highly sensitive optical sive information on the influence of external pressure sensors operating in the infrared range [5], solid-state on the optical properties and band structure [19], the electric current sources [6, 7], and highly sensitive dielectric properties of GaS, GaSe, and InSe crystals strain gauges [8]. Since indium chalcogenide com- [20], the x-ray absorption spectra of InSe [21], and the pounds possess strong anisotropy of chemical bonding, vibrational spectra [22]. However, to the best of my it is possible to modify their physical properties knowledge, first-principles studies of the effect of through intercalation [9]. From the applied standpoint, pressure on the dynamic properties and structure of these compounds are of special interest owing to the InSe crystals have not been performed before. The lack possibility of forming high-quality heterojunctions of detailed x-ray diffraction data on the structural with the use of both van der Waals epitaxy [10Ð12] and transformation under pressure is partially compen- a less laborious mechanical procedure, namely, by sated for with experimental information obtained by bringing them into direct optical contact [13Ð17]. Pellicer-Porres et al. [21]. Unfortunately, the data Moreover, these objects are especially attractive reported in [21] are far from complete, although they from fundamental standpoint. In the last decade, there have made it possible to calculate theoretically the have appeared many works concerned with experimen- effect of pressure on the energy spectrum of charge tal and theoretical investigations of the influence of carriers in the InSe compounds [19]. external pressure on their physical properties. The main A detailed knowledge of changes in the interatomic objective of these experiments is to gain a deeper interactions occurring in indium chalcogenides under

180 RUSHCHANSKIŒ

c 2. CRYSTAL STRUCTURE OF InSe AND THE PRESSURE DEPENDENCE OF THE LATTICE PARAMETERS The crystal structure of InSe was determined using x-ray diffraction in [23, 24]. The known polytypes of ϕ β 4 this crystal are the hexagonal (,D6h P63/mmc), hex- ε 1 γ 5 agonal (D3h , P6m2 ), and trigonal (,C3v R3m) modifications. The γ polytype has been studied most thoroughly. This is explained by the fact that the compounds grown by the Bridgman method crystallize in the γ modification [23]. The rhombohedral unit cell of γ-InSe contains two formula units, which form the Se(1) structure of one layer (Fig. 1). This structure is formed according to the scheme SeÐInÐInÐSe, in which the InÐ Se interaction has an ionicÐcovalent character and the In(2) InÐSe sublayers are linked together by the InÐIn covalent bonds perpendicular to the layer plane. According to the x-ray diffraction investigations performed by In(1) Rigoult et al. [24], each sublayer has an asymmetric (slightly distorted) structure. The displacement of lay- Se(2) ers with respect to each other in the γ modification is described by the vector t = (a + b)/3, where a and b are the basis vectors of the hexagonal unit cell. The lattice parameters and fractional atomic coordinates in the hexagonal setting are listed in Table 1. Se(1) As was shown by Schwarz et al. [25], the γ modification under external pressure is retained up to 10.5 GPa (at room temperature) and then undergoes a In(2) first-order phase transition to a rock-salt-type structure. The NaCl modification possesses metallic properties In(1) (whereas the γ-InSe modification under normal conditions is a semiconductor with band gap Eg = 1.35 eV Se(2) [26]). The compressibility of the γ phase is strongly anisotropic in character: the compressibility is small a and exhibits a nearly linear behavior along the a axis, on the one hand, and is significant and has a nonlinear b behavior along the c axis, on the other. At pressures close to 7 GPa, the structure undergoes progressive Fig. 1. Crystal structure of γ-InSe. The rhombohedral unit irreversible transformations, which manifest them- cell contains two indium and two selenium atoms forming selves in the optical absorption spectra and the vibra- the structure of one layer. Solid lines represent the axes of tional properties. an extended hexagonal cell with three layers of γ-InSe. The most recent data on the pressure dependences of the local environment of selenium atoms in InSe deformations of different types is of more than theoret- crystals were obtained by Pellicer-Porres et al. [21] ical interest, because it becomes possible to thoroughly from an analysis of the x-ray absorption spectra. In my investigate a great variety of problems concerning the opinion, the most important inferences drawn in [21] that can be compared with the theoretical results intercalation, the formation of solid solutions, the obtained in the present work can be summarized as fol- mechanisms of hopping conduction, the elastic proper- lows. ties, the properties governed by deformation effects, the growth of single crystals, and the preparation of thin The pressure dependence of the interatomic dis- films of the studied compounds. In this respect, the pur- tances is adequately described by the first-order equa- pose of the present work was to carry out a first-princi- tion of state [27]: ples theoretical investigation of the structural transfor- ' B' Ð1/3B0 mations and changes in the vibrational properties of an 0 dd= 01 + ----- P , (1) InSe crystal under external hydrostatic pressure. B0

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THE INFLUENCE OF HYDROSTATIC PRESSURE 181

Table 1. Calculated and experimental [24] crystallographic parameters of the γ-InSe structure Atom Experiment Theory Deviation Fractional In(1) 0, 0, 0.00000 0, 0, 0.00043 coordinates In(2) 0, 0, 0.11102 0, 0, 0.11096 Ð0.05% (x, y, z) Se(1) 0, 0, 0.82834 0, 0, 0.82864 Ð0.04% Se(2) 0, 0, 0.61666 0, 0, 0.61599 Ð0.11% a, Å 4.002 3.953 Ð1.2% c, Å 24.946 24.138 Ð3.2% Distances and angles Experiment Theory Deviation

dIn(1)ÐSe(2), Å 2.6258 2.5944 Ð1.2% dIn(1)ÐIn(2), Å 2.7695 2.6678 Ð3.7% dIn(2)ÐSe(1), Å 2.6335 2.5935 Ð1.5% ∠In(1)ÐIn(2)ÐSe(1) 118.673° 118.344° Ð0.27% ∠In(2)ÐIn(1)ÐSe(2) 118.364° 118.388° 0.02% Note: The unit cell parameters and fractional atomic coordinates are given in the hexagonal setting.

where d0 is the interatomic distance under normal con- pseudopotential. The spinÐorbit interaction was not considered in the treatment performed in this work. ditions, B0 is the bulk modulus, and B0' is the derivative of this modulus with respect to pressure. The calculations were carried out with the ABINIT code [32] involving the pseudopotential and plane- The pressure dependence of the InÐSe distance (at wave basis sets and based on an efficient fast Fourier pressures of less than or equal to 7.1 GPa) is described transform algorithm [33] (for transforming wave func- by the following parameters: d0 = 2.634 Å and B0 = tions between the real and reciprocal spaces), the con- ± 116 20 GPa for B0' = 5. At pressures above 7.1 GPa, jugate-gradient band method [34], the potential-based the InÐSe distance jumpwise increases and becomes conjugate-gradient algorithm, which made it possible equal to approximately 2.7 Å at 10 GPa. The parameter to determine the self-consistent potential [35], and the a of the hexagonal lattice is characterized by a stronger perturbation-theory algorithms. Details of the computa- dependence on the pressure (B = 44 GPa for B' = 5). tion of the responses to atomic displacements and 0 0 homogeneous electric fields are given in [36]. Subse- The InÐInÐSe angle calculated at 10 GPa is equal to ° ° quent calculations of the dynamic matrices, Born effec- 121.4 (under normal conditions, this angle is 118.7 ). tive charges, permittivity tensors, and interatomic force constants are described in [37]. 3. DESCRIPTION OF THE METHOD Integration over the Brillouin zone was performed by the special-point method [38] with the use of six The ground state and vibrational properties were points in the irreducible region of the Brillouin zone. investigated in the plane-wave approximation of the The basis set of plane waves was limited by a maximum density-functional theory [28]. The calculations were kinetic energy of 20 Ry. The chosen basis set was ana- carried out with nonlocal norm-conserving ab initio lyzed for sufficiency. It was demonstrated that, upon pseudopotentials in the form proposed by Hartwigsen the inclusion of 19 special points of integration and the et al. [29]. The 5s25p1 and 4s24p4 electron configura- choice of the maximum kinetic energy equal to 30 Ry, tions were used for valence electrons of indium and a change in the calculated frequency of vibrational selenium atoms, respectively. The exchangeÐcorrela- modes was no more than 0.5 cmÐ1. Therefore, the cal- tion interaction was included in the local-density culations were carried out in the region of convergence. approximation in the parametric form [30], which reproduces the exact results of the quantum-mechanical calculations for a homogeneous electron gas [31]. The 4. RESULTS AND DISCUSSION nonlocality of the pseudopotentials was taken into 4.1. Static Properties account by components for the s, p, and d channels. The s channel of the corresponding potential was used as a The total energy of the InSe system was calculated local component. The nonlinear character of the as a function of the unit cell volume in the range from exchangeÐcorrelation interaction of the valence elec- an experimental unit cell volume of 115.29 Å3 to 60% trons with electrons of the atomic core and the relativ- of this value. The results of these calculations are pre- istic effects for core electrons were allowed for in the sented in Fig. 2.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 182 RUSHCHANSKIŒ

1.0 Let us now consider the pressure dependences of the 16 crystallographic parameters (Fig. 3). It can be seen from Fig. 3a that the pressure dependences of the interatomic distances d and d exhibit a monotonic 14 InÐIn InÐSe 0.8 behavior and are well approximated by the first-order equation of state (1) with parameters B0InÐSe = 82 GPa 12 and B0InÐIn = 57 GPa (in both cases, the parameter B0' is 0.6 equal to five for adequate comparison with the available 10 experimental data). Although the calculated parameter ± BInÐSe differs from the experimental value (116 V 8 20 GPa [21]), this disagreement can be explained by , e GPa E 0.4 the nonmonotonic experimental dependence dInÐSe(P) 6 P, in the range of pressures close to 4 GPa (Fig. 3a, curve 3). The parameter B0InÐSe = 116 GPa was obtained by aver- 4 aging the experimental values up to 7 GPa, whereas this 0.2 dependence in the pressure range up to 4 GPa is steeper than the averaged dependence. Therefore, the depen- 2 dence at low pressures should be described by a smaller value of B0InÐSe. As can be seen from Fig. 3a, the slope 0 0 of the calculated pressure dependence of the InÐSe bond length agrees with the slope of the experimental –2 curve up to a pressure of 3 GPa despite the small error 80 90 100 110 120 3 in the determination of the bond length. V, Å The pressure dependence of the InÐIn interatomic Fig. 2. Dependences E(V) and P(V). The vertical arrow indi- distance is characterized by the parameter B0InÐIn. This cates the position of the theoretically calculated equilibrium parameter is smaller than the corresponding parameter configuration. Symbols are the calculated values of E(V). The solid line represents the dependence E(V) approxi- for the InÐSe bond, which indicates a low rigidity of the mated by the first-order equation of state (2). The dashed InÐIn bond. This fact is in complete agreement with the line corresponds to the dependence P(V). data on the lattice dynamics in InSe crystals [40], according to which the force constant of the InÐSe bond is larger than that of the InÐIn bond. The dependence E(V) is adequately described by the The dependence of the parameter a of the hexagonal first-order equation of state [27]: lattice on the pressure exhibits a smooth behavior up to ' 7 GPa corresponds to the bulk modulus B = 44 GPa ()B0 0 B0V V 0/V B0V 0 ∂ (Fig. 3b). This is in complete agreement with the exper- EE= 0 + ------1+ Ð ------, “ Ù 4F3 B0' B0' Ð 1 B0' Ð 1 imental data. However, in the pressure range from 7 to 11 GPa, the calculated pressure dependence becomes α where V = 108.9 Å3 is the equilibrium volume, B = steeper. The dependence of the angle of the rhombo- 0 0 hedral unit cell on the pressure (Fig. 3c) is also charac- 29 GPa, and B0' = 6.2. Setting B0' = 5, we obtain V0 = terized by a specific feature (a decrease in the angle α) 3 108.47 Å and B0 = 34 GPa. in the pressure range 7Ð11 GPa. The calculated equilibrium volume differs from the The distance between the selenium atoms of different experimental value (at 300 K [24]) by 5.5%. This dis- layers monotonically decreases over the entire pressure crepancy is characteristic of calculations performed in range and is adequately described by expression (1) with the local-density approximation for exchangeÐcorrela- parameters B0 = 9 GPa and B0' = 3.8 (or B0 = 7.3 GPa tion interactions. The crystallographic parameters for the at B' = 5, but with a considerably larger error). calculated equilibrium configuration and the relevant 0 experimental data are compared in Table 1. As can be As could be expected, the bulk modulus for the pres- seen from this table, the fractional coordinates are repro- sure dependence of parameter c of the hexagonal unit duced with a reasonable accuracy. The decrease in the cell is substantially smaller than that of parameter a. In calculated interatomic distances as compared to the the range from 7 to 11 GPa, the pressure dependence of experimental values is associated with the decrease in the parameter c is nonmonotonic and the parameter itself unit cell parameters due to the use of the local-density remains almost unchanged. Therefore, the decrease in approximation alone in our calculations. The inclusion the unit cell volume at these pressures is primarily due of this approximation especially affects the length of the to the decrease in parameter a. However, at pressures InÐIn covalent bond, which is characterized by a nonuni- above 11 GPa, the pressure dependence regains its ini- form distribution of the valence electron density [39]. tial behavior and parameter c decreases monotonically.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 THE INFLUENCE OF HYDROSTATIC PRESSURE 183

2.700 24.5 4.0 (a) (b) 2.675

24.0 3.9 2.650

2.625 23.5 3.8 2.600 Å Å Å , , , c d 2.575 a 23.0 3.7 2.550

2.525 22.5 3.6 1 1 2 2 2.500 3

2.475 22.0 3.5 0142461012 8 0142461012 8 P, GPa P, GPa 29.5 122 3.0 (c) (d) 5.20 1 2.9 2 29.0 121 2.8 5.15

2.7 28.5 120 Å ,

Å 2.6 5.10 , , deg , deg d Se–Se ϕ α d 28.0 119 2.5 5.05 2.4 27.5 118 1 2 2.3 5.00

27.0 117 2.2 0142461012 8 0142461012 8 P, GPa P, GPa Fig. 3. Pressure dependences of the crystallographic parameters of the γ-InSe structure. (a) (1, 2) Calculated and (3) experimental [21] pressure dependences of the interatomic distances (1, 3) dInÐSe and (2) dInÐIn. (b) Pressure dependences of the unit cell parameters (1) a and (2) c in the hexagonal setting. (c) Pressure dependences of (1) the angle ϕ and (2) the angle α between the basis vectors of the unit cell in the rhombohedral setting. (d) Pressure dependences of (1) the layer thickness dSeÐSe and (2) the distance between adjacent layers. Dashed lines indicate the pressure range from 7 to 11 GPa in which the pressure dependences exhibit spe- ciﬁc features associated with the structural transformations.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 184 RUSHCHANSKIŒ

280 again decreases. Speciﬁc features at these pressures can also be observed in the pressure dependence of the angle ϕ between the InÐIn and InÐSe bonds (Fig. 1). It 260 can be seen from Fig. 3c that the pressure dependence of the angle ϕ, even though monotonic, is far from linear, as was assumed in [19]. The calculated angle ϕ at a 240 pressure of 10 GPa is equal to 121.1° (the experimental estimate of ϕ is 121.4° [24]). Under equilibrium conditions, this angle is calculated to be ϕ = 118.4° (the 220 experimental value of ϕ at 300 K is 118.7°). A compar- ϕ ison of the dependences dSeÐSe(P) and (P) shows that the layer thickness increases in the ranges of pressures 200 at which the angle ϕ increases signiﬁcantly, i.e., at approximately 2 GPa and from 7 to 11 GPa. It is these considerable changes in the angle ϕ (against the back- 180 ground of a monotonic decrease in the InÐSe and InÐIn interatomic distances) that are responsible for the increase in the layer thickness. –1 160

, cm Therefore, in the range of the experimentally

ω observed phase transformation (7Ð11 GPa), the calcu- 140 lated dependences of the parameters a and c exhibit an anomalous behavior. This manifests itself in the fact that the rigidity of the lattice decreases along the direc- 120 tion of the strong bond and increases along the direction perpendicular to the layers. 1 100 2 The possible mechanism of the pressure-induced 3 phase transition in InSe was considered by Pellicer- 4 Porres et al. [21], who proposed the following evolu- 80 tion of the structure in the course of the phase transformation into the NaCl modiﬁcation. As follows from the experimental data (see [21] and references therein), 60 under a pressure of approximately 7 GPa at room temperature, there arise local vibrations and the number of free charge carriers increases. These irreversible pro- 40 cesses are associated with the breaking of InÐIn bonds, i.e., with the formation of defect states. An increase in 010123456789 11 the pressure leads to an increase in the concentration of P, GPa free charge carriers, which is explained by the increase in the number of broken InÐIn bonds. According to the Fig. 4. Theoretical and experimental [22] dependences of estimates, at a pressure of 10 GPa, there are ten unit the vibrational frequencies on the external hydrostatic pres- cells for each defect state. At pressures above 10 GPa, sure for the γ-InSe crystal: (1) calculated frequencies of the experimentally observed vibrational modes, (2) experimen- the material undergoes a transformation throughout the tal frequencies of the observed vibrational modes, bulk with the formation of a NaCl-type structure. An (3) experimental frequencies of the additional mode important role in this transformation is played by induced at a pressure of 7 GPa and retained after decom- atomic vibrations. In particular, annealing at a temper- pression, and (4) calculated frequencies of the experimen- ° tally unobservable modes. ature of 250 C and a pressure of only 4 GPa results in a structural transformation [22]. Since the properties of the ground state were determined in terms of the den- The calculated pressure dependence of the layer sity-functional theory at absolute zero temperature, our thickness (or, what is the same, the distance between calculations did not reveal structural transformation. the selenium atoms of the same layer) exhibits nonlin- However, the anomalies observed in the pressure ear behavior (Fig. 3d). As the pressure increases, the dependences of the crystallographic parameters are layer thickness remains nearly constant at pressures most likely caused by the formation of defects due to atomic vibrations at nonzero temperatures. below 1.5 GPa, drastically increases at ~2 GPa, and then monotonically decreases in the pressure range up It should be noted that, at a pressure of 10 GPa, the to ~7 GPa. Above this pressure, the layer thickness volume decreases by 16% with respect to the equilib- increases to an equilibrium value (at ~11 GPa) and then rium volume. This also agrees well with the experimen-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 THE INFLUENCE OF HYDROSTATIC PRESSURE 185

Table 2. Calculated and experimental vibrational frequencies for the γ-InSe crystal

Reference EAEETO ELO ATO ALO A This work, ω (cmÐ1) 43.68 108.10 172.46 175.18 210.63 189.47 190.0 227.21 [42] 178 212 190 199 [43] 173 205 191 199 [44] 178 210 189 198 [45] 178 214 202 203 [22] 40.3 115.8 177 208.2 199.7 226.3 Rigid modes Intralayer vibrations ∂ω/∂P (cmÐ1/GPa) [22] 0.68 ± 0.24 5.41 ± 0.28 4.27 ± 0.24 3.60 ± 0.15 3.32 ± 0.22 4.33 ± 0.20 ∂ω/∂P (cmÐ1/GPa) (this work) 0.84 5.45 4.45 2.97 3.99 4.23 ∂2ω/∂P2 (cmÐ1/GPa2) [22] Ð0.01 ± 0.02 Ð0.10 ± 0.03 Ð0.9 ± Ð Ð0.01 ± 0.02 Ð0.06 ± 0.02 0.02 ∂2ω/∂P2 (cmÐ1/GPa2) (this work) Ð0.02 Ð0.11 Ð0.10 Ð0.06 Ð0.07 Ð0.07 tally determined decrease in the volume (14.8%) upon results obtained (Table 2) shows that the calculated the phase transition [25]. vibrational frequencies and their pressure dependences are in good agreement with the experimental data. Although the low-frequency rigid mode E attributed 4.2. Dynamic Properties to slip displacements of the layers with respect to each The occurrence of structural transformations in the other is well reproduced, the frequency of the mode A InSe compound under hydrostatic pressure was inde- that corresponds to opposite displacements of the lay- pendently confirmed by the experimental data on the ers as a whole along the direction of the weak bond is influence of pressure on the Raman spectra obtained by slightly underestimated. This discrepancy can be Ulrich et al. [22]. As was noted above, apart from the explained by the use of the local-density approxima- vibrational modes observed in the γ-InSe crystal under tion, which does not include the van der Waals interac- normal conditions, the Raman spectra exhibit vibration. Most likely, additional allowance made for the van tions at a frequency of approximately 165 cmÐ1, which der Waals attraction involved in the interlayer interac- arise at pressures above 7 GPa and persist after decom- tion should result in a somewhat larger value of the pression (with the corresponding decrease in the fre- interlayer force constant and in complete agreement quency; see Fig. 4). This mode was assigned to local between the calculated and experimental data. Another vibrations associated with structural defects that reason for this discrepancy is that the calculated fre- encourage phase transformation at a pressure of quencies were determined at absolute zero temperature, ~10 GPa [25]. whereas the experimental data were obtained at room temperature. Since the mode under consideration is The influence of pressure on the vibrational spec- characterized by a strong anharmonicity (as follows trum was not analyzed theoretically in [22]. With the from the dependences depicted in Fig. 4 and the values aim of determining the mode symmetry and identifying of ∂ω/∂P in Table 2), the above circumstance can also two-photon processes, the phonon dispersion was cal- explain the underestimated frequency of the A mode. culated in [22] in the framework of the rigid-ion model [41]. Panella et al. [11] examined the interface modes It is worth noting that the frequency of the longitu- in an InSe/Si(111)-(1 × 1)ÐH heterojunction and car- dinal mode A associated with the opposite displace- ried out first-principles calculations of the phonon ments of the InÐSe sublayers with respect to each other spectrum of the InSe crystal. However, to the best of my along the direction of the weak bond is underestimated knowledge, first-principles investigations of the pres- by 8Ð10 cmÐ1, even though all the other experimental sure dependences of the vibrational modes have never data are well reproduced. The calculated value of the been performed. In the present work, I carried out these LOÐTO splitting is of the order of 1 cmÐ1. According to calculations using available experimental data in order the majority of experimental works, the splitting is to confirm the reliability of the calculated static charac- approximately equal to 9 cmÐ1. On the other hand, Jandl teristics. et al. [45] experimentally obtained a splitting of Ð1 The results of these calculations are presented in approximately 1 cm (but, in this case, the frequency Ð1 Table 2 and Fig. 4. The equilibrium configuration cor- of the TO mode was 202 cm ). responding to a minimum in the dependence E(V) was The calculated pressure dependences of the vibra- used as the initial configuration. A comparison of the tional frequencies and the available experimental data

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 186 RUSHCHANSKIŒ are in good agreement. The sole exception is provided hydrostatic pressure. The results of the calculations are by the aforementioned two modes. However, the pres- in good agreement with the available experimental sure dependences of these modes also agree well with data. the experimental data, except for systematic deviation The results obtained in this work can be used both as of the calculated frequencies from the experimental fre- initial data for detailed theoretical investigations and in quencies toward the low-energy range. the interpretation of experimental data on the pressure The pressure dependences of the frequency of the dependences of the crystallographic parameters, the experimentally unobservable modes are also plotted in electronic and vibrational properties of γ-InSe, the Fig. 4. Under equilibrium conditions, no LOÐTO split- deformation potentials, etc. ting occurs in the E mode. However, this mode is split with an increase in the pressure and, at 11 GPa, the splitting is approximately equal to 9 cmÐ1. It can be seen REFERENCES from Fig. 4 that, in the pressure range from 3 to 7 GPa, 1. L. I. Man, R. K. Karakhanyan, and R. M. Imamov, Kri- stallografiya 6, 1166 (1974). the frequency of the ATO mode increases more slowly than the frequencies of the other vibrations. Since the 2. R. S. Putnam and D. G. Lancaster, Appl. Opt. 38, 1513 frequency of this mode is predominantly determined by (1999). the InÐIn interatomic interaction between two InÐSe 3. R. A. Kaindl, F. Eickemeyer, M. Woerner, and sublayers, the above finding is indirect evidence in T. Elsaesser, Appl. Phys. Lett. 75, 1060 (1999). favor of the hypothesis that the formation of defect 4. J. P. Martinez, A. Segura, J. L. Waldes, and A. Chevy, states is associated with the breaking of InÐIn bonds. J. Appl. Phys. 62, 1477 (1987). It should be noted that all frequencies of the lattice 5. V. N. Katerinchuk, M. É. Kovalyuk, and A. D. Ogorod- vibrations exhibit a smooth monotonic dependence on nik, Neorg. Mater. 32, 937 (1996). the pressure. The calculations performed within simple 6. C. Julien, M. Jouanne, P. A. Burre, and M. Balkanski, models of the lattice dynamics of the studied crystal Solid State Ionics 28Ð30, 1167 (1988). (for example, in terms of the simplest chain model [40, 7. M. Balkanskii, P. Gomes da Costa, and R. F. Wallis, 41]) demonstrate that good agreement between the Phys. Status Solidi B 194, 175 (1996). experimental and theoretical vibrational frequencies 8. V. V. Dragomeretskiœ, Z. D. Kovalyuk, V. K. Kiva, and can be achieved even in the model of axially symmetric A. I. Seredyuk, USSR Inventor’s Certificate No. 178,511. force constants, which disregard the elasticity of flex- 9. P. Gomes da Costa, M. Balkanski, and R. F. Wallis, Phys. ure of the valence bond and are determined primarily Rev. B 43, 7066 (1991). by the rigidity of the InÐIn and InÐSe bonds and the van 10. M. O. D. Camara, A. Mauger, and I. Devos, Phys. Rev. B der Waals interaction between selenium atoms of dif- 65, 205308 (2002). ferent layers. Since the aforementioned interatomic dis- 11. V. Panella, A. L. Glebov, J. P. Toennis, et al., Phys. Rev. tances monotonically change under pressure (Fig. 3a, B 59, 15772 (1999). curves 1, 2; Fig. 3d, curve 2), the frequencies of lattice 12. E. Wisotzki, A. Klein, and W. Jaegermann, Thin Solid vibrations are also characterized by a smooth depen- Films 380, 263 (2000). dence. 13. E. P. Zaretskaya, V. F. Gremenok, Y. V. Rud, et al., Dif- In general, the above results are indirect evidence in fus. Defect Data, Part B: Solid State Phenom. 80Ð81, 293 support of the reliability of the data obtained in the pre- (2001). ceding section on the structural transformations under 14. V. N. Katerinchuk, Z. D. Kovalyuk, T. V. Betsa, et al., hydrostatic pressure. Pis’ma Zh. Tekh. Fiz. 27 (4), 62 (2001) [Tech. Phys. Lett. 27, 424 (2001)]. 15. Yu. A. Nikolaev, V. Yu. Rud, and E. I. Terukov, Semicon- 5. CONCLUSIONS ductors 34, 677 (2000). Thus, the structural transformations of the γ-InSe 16. V. N. Katerinchuk, Z. D. Kovalyuk, V. V. Netyaga, and crystal under hydrostatic pressure were investigated T. V. Betsa, Pis’ma Zh. Tekh. Fiz. 26 (17), 6 (2000) theoretically. It was demonstrated that the dependence [Tech. Phys. Lett. 26, 754 (2000)]. E(V) is adequately described by the first-order equation 17. V. N. Katerinchuk, Z. D. Kovalyuk, and A. L. Ogorod- of state. The calculated bulk modulus of the γ-InSe nik, Fiz. Tekh. Poluprovodn. (St. Petersburg) 28, 2096 (1994) [Semiconductors 28, 1157 (1994)]. crystal is equal to 29 GPa at B' = 6.2. The pressure 0 18. Yu. M. Orishchin and I. M. Stakhira, Fiz. Tekh. Polupro- dependences of the lattice parameters of the γ-InSe vodn. (Leningrad) 10, 2111 (1976) [Sov. Phys. Semi- crystal exhibit a nonmonotonic behavior in the range 7Ð cond. 10, 1256 (1976)]. 11 GPa. The layer thickness is also characterized by a 19. F. J. Manjón, D. Errandonea, A. Segura, et al., Phys. Rev. nonmonotonic pressure dependence with specific fea- B 63, 125330 (2001). tures at a pressure of 2 GPa and in the range 7Ð11 GPa. 20. D. Errandonea, A. Segura, V. Munoz, and A. Chevy, The vibrational properties of the crystal and the fre- Phys. Rev. B 60, 15866 (1999). quencies of lattice vibrations at the center of the Bril- 21. J. Pellicer-Porres, A. Segura, V. Munoz, and A. San Miguel, louin zone were investigated as a function of external Phys. Rev. B 60, 3757 (1999).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 THE INFLUENCE OF HYDROSTATIC PRESSURE 187

22. C. Ulrich, M. A. Mroginski, A. R. Goni, et al., Phys. Sta- 34. M. C. Payne, M. P. Teter, D. C. Allan, et al., Rev. Mod. tus Solidi B 198, 121 (1996). Phys. 64, 1045 (1992). 23. L. I. Man, R. M. Imamov, and S. A. Semiletov, Kristal- 35. X. Gonze, Phys. Rev. B 54, 4383 (1996). lograﬁya 21, 628 (1976) [Sov. Phys. Crystallogr. 21, 355 36. X. Gonze, Phys. Rev. B 55, 10337 (1997). (1976)]. 37. X. Gonze and C. Lee, Phys. Rev. B 55, 10355 (1997). 24. J. Rigoult, A. Rimsky, and A. Kuhn, Acta Crystallogr. B 38. H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 36, 916 (1980). (1976). 25. U. Schwarz, A. R. Goni, K. Syassen, et al., High Press. 39. P. Gomes da Costa, R. G. Dandrea, R. F. Wallis, and Res. 8, 396 (1991). M. Balkanski, Phys. Rev. B 48, 14135 (1993). 26. M. Balkanskii, C. Julien, and M. Jouanne, J. Power 40. T. Ikari, S. Shigetomi, and K. Hashimoto, Phys. Status Sources 20, 213 (1987). Solidi B 111, 477 (1982). 27. F. D. Murnaghan, Proc. Natl. Acad. Sci. USA 30, 244 41. P. Brüesch, Phonons: Theory and Experiments, Vol. 1: (1944). Lattice Dynamics and Models of Interatomic Forces 28. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). (Springer-Verlag, Berlin, 1982). 29. C. Hartwigsen, S. Goedecker, and J. Hutter, Phys. Rev. B 42. C. Julien, M. Eddrief, M. Balkanski, and A. Chevy, Phys. 58, 3641 (1998). Rev. B 46, 2435 (1992). 30. J. P. Perdew and Y. Wang, Phys. Rev. B 33, 8800 (1986). 43. N. M. Gasanly, B. M. Yvadov, V. I. Taganov, and 31. D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 E. A. Vinogradov, Phys. Status Solidi B 89, K43 (1978). (1980). 44. K. R. Allakhverdiev, S. S. Babaev, E. Y. Salaev, and 32. The ABINIT Code is a Common Project of the Univer- M. M. Tagyev, Phys. Status Solidi B 96, 177 (1979). site Catholique de Louvain, Corning Incorporated, and 45. S. Jandl, M. Banville, and J. Deslandes, Can. J. Phys. 59, Other Contributors, URL http://www.pcpm.ucl.ac.be/ 198 (1981). abinit. 33. S. Goedecker, SIAM J. Sci. Comput. (USA) 18, 1605 (1997). Translated by O. Borovik-Romanova

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 188Ð191. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 185Ð188. Original Russian Text Copyright © 2004 by Malyshev, Peshev, Pritulov.

MAGNETISM AND FERROELECTRICITY

Temperature Dependences of the Dielectric Properties of LithiumÐTitanium Ferrite Ceramics A. V. Malyshev, V. V. Peshev, and A. M. Pritulov Tomsk Polytechnical University, pr. Lenina 30, Tomsk, 634034 Russia e-mail: [email protected] Received December 10, 2002; in ﬁnal form, May 13, 2003

Abstract—Temperature dependences of the real ε' and imaginary ε'' parts of the complex permittivity of lith- iumÐtitanium ferrite ceramics are measured in the frequency range 102Ð106 Hz at different test-signal amplitudes and dc bias voltages. It is found that the dielectric characteristics of the ceramic samples drastically change in narrow temperature ranges. The assumption is made that relaxators whose reorientation is due to tunneling transitions of electrons inside “bivalent iron ionÐtrivalent metal ion” pairs are involved in polarization processes. Under certain conditions, the reorientation of relaxators can have collective character. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION be expected that the characteristic time of polarization will depend not only on the temperature but also on the It is known that the conductivity σ and complex per- time of action of the polarizing field (or, in the case of mittivity ε* substantially affect the propagation of elec- an ac electric field, on the frequency) and its strength. tromagnetic waves in ferrite materials and, hence, can It is known that electric dipoles at high concentra- be responsible for the functional properties of ferrite- tions bring about the spontaneous formation of electric based devices. At present, there are many works con- 2+ cerned with the electrical properties of ferrites [1Ð10]. domains. Since the Fe content varies over a wide As a rule, dependences of the conductivity σ and com- range, the concentrations of dipoles can also change ε significantly. It can be assumed that the high permittiv- plex permittivity * on the frequency f and temperature ε T for polycrystalline ferrites are interpreted within ity for ferrites is caused not only by the interlayer either the model of interlayer polarization [1] or the polarization but also by the polarization due to either model of interlayer polarization involving surface individual recharging of ion pairs, recharging of pairs states of grain boundaries [2]. Since interlayer polariza- involved in spontaneously formed electric domains, or tion is caused primarily by charge transfer, the charge recharging of pairs contained in domains induced by transfer mechanism affects the characteristics of the the electric field. interlayer polarization. It is believed that charge trans- The aim of this work was to elucidate the possible fer proceeds either through migration of charge carriers mechanism of relaxation polarization in lithiumÐtita- over the impurity band [3, 4] or through hoppings of nium ferrite ceramics. For this purpose, we investigated carriers over localized energy levels due to electronÐ the temperature dependences of the real ε' and imagi- phonon interactions [5]. The hopping mechanism of nary ε'' parts of the complex permittivity at different charge transfer in ferrites is associated with the pres- frequencies and amplitudes of the test signal in the ence of bivalent iron ions and electron transitions presence and absence of a dc bias voltage. between variable-valence ions, for example, Fe2+ + Me3+ Fe3+ + Me2+ [6]. It has been established that 2. SAMPLES AND EXPERIMENTAL TECHNIQUE the higher the Fe2+ concentration, the higher the conductivity and the larger the real part ε' of the permittiv- In our experiments, we used ferrites of composition ity. On this basis, it has been assumed that these transi- Li0.649Fe1.598Ti0.5Zn0.2Mn0.051O4 doped with 0.22 wt % tions are responsible for charge transfer and polariza- Bi2O3. Samples were synthesized under working condition [7Ð9]. In this case, there is no need to invoke the tions according to the ceramic technique and were then Koops model, because the recharging of ion pairs sintered in air at T = 1280 K for 120 min. After sinter- Fe2+ + Me3+ Fe3+ + Me2+ can be considered as the ing, the samples were ground on both sides from the reorientation of dipoles in an ac electric field. Since the initial thickness d = 1 mm to a thickness of 0.22 mm. components of ion pairs are crystal-forming ions, the As a result, the samples had the form of pellets 13 mm large value of ε' can be explained by the high concen- in diameter. Then, silver contacts were applied to the tration of ion pairs. When electron transitions in these sample surface through thermal evaporation under vac- pairs occur through phonon-assisted tunneling, it can uum. The diameter of the measuring contact was equal

TEMPERATURE DEPENDENCES OF THE DIELECTRIC PROPERTIES 189 to 5 mm. The pellets with contacts were subjected to normalizing annealing at T = 570 K for t = 1 h. The (a) magnetic Curie temperature T for the ferrite ceramics C 1' thus prepared was equal to 575 K. We measured the 103 capacitance C and conductance G, i.e., the conductivity 1 governed by both conduction current and the polarization current component coinciding in phase with the 2 electric ﬁeld. The measurements were carried out in the temperature range 300Ð600 K. In the course of measurements, the samples were heated and cooled at a rate 102 3 ', rel. units of 2 K/min. The experiments were performed at test- ε signal frequencies f = 100, 103, 104 (an E7-14 bridge), and 106 Hz (an E7-12 bridge). The real ε' and imaginary 4 ε'' parts of the permittivity were calculated from the ε ε δ ω standard formulas: ' = Cd/(S 0), tan = G/( C), and TC ε'' = ε'tanδ, where ε is the permittivity of free space, ω 101 0 300400 500 600 is the circular frequency of the polarizing ﬁeld, and tanδ is the dielectric loss tangent. 106 (b) 5 3. RESULTS AND DISCUSSION 6 104 The temperature dependences of the real ε' and 7 imaginary ε'' parts of the complex permittivity mea- 2 10 8 sured at a test-signal amplitude Utest = 56 mV are

'', rel. units 0 depicted in Fig. 1. It can be seen from Fig. 1a that the ε 10 polarization involves no less than two stages and the permittivity ε' = F(T) at saturation (ε' ) for the low- 10–2 sf 300400 500 600 temperature stage depends on the frequency and T, K decreases with an increase in the frequency. Below, we will consider only the most pronounced low-tempera- Fig. 1. Temperature dependences of (a) real ε' and (b) imag- ture stage. The absence of relaxation peaks in the inary ε'' parts of the complex permittivity measured at the ε dependences '' = F(T) (Fig. 1b) suggests that the con- test-signal amplitude Utest = 56 mV in the course of (1Ð8) duction current substantially exceeds the active compo- heating and (1') cooling. Frequency: (1, 1', 5) 102, (2, 6) 103, nent of the relaxation current. The temperature depen- (3, 7) 104, and (4, 8) 106 Hz. dences of the conductance G(T) used for calculating the values of ε'' are virtually independent of the frequency. The measurements were performed during heating and The data presented in Fig. 1a cannot be explained in cooling of the samples. The curves ε'' = F(T) measured the framework of the Debye model, because the value in the course of heating and cooling coincide with each ε' other. The dependences ε' = F(T) are characterized by of sf depends on the frequency. Recall that, within the an insignificant hysteresis at a frequency of 100 Hz, Debye model, the relaxation time τ(T) does not depend which decreases with an increase in the frequency. on the duration of the polarizing voltage pulse and, Note that the temperature dependences of the per- hence, on the test-signal frequency. Consequently, the ε ε mittivity ε' can be well approximated within the model value of sf' is equal to the static permittivity s and does of interlayer polarization. In this case, the conduction not depend on the frequency f, even though there are current is dominant; therefore, the activation energy of distributions of the activation energy Ea and preexpo- relaxation E should be equal to the activation energy of τ τ a nential factor 0. Therefore, for (T) = const( f ), at any charge transfer Eaσ. The activation energy Ea, which is test-signal frequency, there always (theoretically) exists determined from the dependences ε'(T) in the frame- a temperature range in which virtually all relaxators are work of this model, is equal to 0.36Ð0.38 eV. However, involved in the reorientation and the permittivity ε' the dependences ε''(T) can be described only at activa- reaches the same value ε . ≠ s tion energies E = (0.7Ð0.74) eV > Ea. Since Ea Eaσ and the temperature dependences of the conductance In the case when the polarization is caused by either G(T) for the studied samples are almost identical at dif- the reorientation of electric domains in ferroelectrics ferent frequencies, the experimental temperature [11] or the reorientation of relaxators due to tunneling dependences of the real ε' and imaginary ε'' parts of the of charge carriers [5] between centers of localization, permittivity and also the large values of ε' have defied the number of dipoles involved in this process is limited explanation in terms of interlayer polarization. by the duration of polarizing-field action. Under these

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 190 MALYSHEV et al.

(a) 103 (a) 1' 104 1 2' 1 2 2 3 3 1', 2', 3' 10 4, 4'

2 10 ', rel. units

3 ε ', rel. units ε 102

4 400 500 600 TC 101 (b) 300400 500 600 105 5 5 6 6 (b) 10 6 7 7 104 8, 5'–8'

104 '', rel. units ε 8 102 103

'', rel. units 400 500 600 ε T, K 100 ε –2 Fig. 3. Temperature dependences of (a) real ' and (b) imag- 10 ε 300400 500 600 inary '' parts of the complex permittivity measured at the test-signal amplitude U = 56 mV and frequency f = T, K test 103 Hz in the course of (1Ð8) heating and (1'Ð8') cooling at dc polarizing voltages U : (1, 1', 5, 5') 0.2, (2, 2', 6, 6') 0.25, ε p Fig. 2. Temperature dependences of (a) real ' and (b) imag- (3, 3', 7, 7') 0.3, and (4, 4', 8, 8') 0 V. inary ε'' parts of the complex permittivity measured at the test-signal amplitude Utest = 2800 mV in the course of (1Ð 8) heating and (1', 2') cooling. Frequency: (1, 1', 5) 102, (2, 3 4 6 and a low frequency is applied to the sample, the con- 2', 6) 10 , (3, 7) 10 , and (4, 8) 10 Hz. centration of dipoles oriented along the same direction can reach large values in certain time intervals. The conditions, the real part of the permittivity at saturation interaction between dipoles within these intervals can lead to specific features in the behavior of polarization ε sf' is a decreasing function of the frequency (see (due to the collective reorientation of the dipoles) and, Fig. 1a). possibly, to the formation of electric domains. Thus, we believe that the features revealed in the temperature In order to elucidate the influence of the polarizing- ε field strength of the permittivity, we measured the tem- dependences of the permittivity ' are associated with perature dependences of ε' and ε'' at the same frequen- the collective character of the dipole reorientation during part of the half-cycle of the ac electric field. To put cies and the test-signal amplitude Utest = 2800 mV (Fig. 2). As can be seen from Fig. 2a, the dependences it differently, the electric field at regular intervals ε' = F(T) have a considerable hysteresis at a frequency induces a ferroelectric-like state in the dipole system. of 100 Hz, which decreases with an increase in the fre- In this respect, it is of interest to investigate the tem- quency. These dependences exhibit an anomalous perature dependences of the dielectric properties under behavior, which manifests itself in a drastic decrease in conditions where the dc polarizing voltage Up and the the values of ε' with an increase in the temperature ac test-signal voltage Utest = 56 mV < Up are applied to beginning with T = 550 K (Fig. 2a, curves 1, 1'). the sample. In this case, the test signal does not change The hysteresis observed in the dependence ε' = the state of the dipole system and serves only for test- F(T) and a sharp decrease in the values of ε' (Fig. 2a, ing, whereas the concentration of dipoles oriented by curves 1, 1') indicate that the ferrite possibly possess the dc electric field does not depend on the test-signal ferroelectric-like properties. However, these features frequency. It can be expected that, at a dc polarizing are observed only at a high test-signal amplitude Utest = voltage Up, the specific features in the temperature 2.8 V and a long duration of polarizing-field action ( f = dependences of the dielectric characteristics should be 100 Hz). When an ac electric field with a high strength observed at frequencies f > 100 Hz (unlike the depen-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 TEMPERATURE DEPENDENCES OF THE DIELECTRIC PROPERTIES 191

(a) voltage U . Similar features are observed in the temper- 3 p 200 3' ature dependences of the dielectric characteristics mea- 103 sured at a frequency of 10 kHz (Fig. 4). As was 100 2' expected, the temperatures Tstart and Tend at f = 10 kHz are equal to those at f = 1 kHz; i.e., these temperatures ' 1 depend on the dc polarizing voltage Up and are independent of the frequency f at low test-signal voltages 1 ', rel. units 460 480 U . The inset shows the speciﬁc features in the depen- ε test 2 2 ε 10 3 dences '(T) measured during cooling. 4, 1'–4' 4. CONCLUSIONS Thus, it was established that the activation energy of 400 500 600 relaxation polarization differs from the activation energy of charge transfer and that the conductivity does (b) 105 not depend on the frequency. This means that the inter- 5 layer polarization makes an insigniﬁcant contribution 6 to the high permittivity ε' in the frequency and temper- 104 7 8, 5'–8' ature ranges covered. It is found that the dielectric char-

'', rel. units acteristics of the ceramic samples drastically change in ε 103 narrow temperature ranges. The features observed in the temperature dependences of the dielectric charac- 102 teristics can be associated with the collective reorienta- 400 500 600 tion of dipoles; in turn, the collective polarization is T, K most likely induced by the electric ﬁeld.

Fig. 4. Temperature dependences of (a) real ε' and (b) imaginary ε'' parts of the complex permittivity measured at the REFERENCES test-signal amplitude U = 56 mV and frequency f = test 1. G. G. Koops, Phys. Rev. 83 (1), 121 (1951). 104 Hz in the course of (1Ð8) heating and (1'Ð8') cooling at 2. V. P. Miroshkin, Ya. I. Panova, and V. V. Pasynkov, Phys. dc polarizing voltages Up: (1, 1', 5, 5') 0.2, (2, 2', 6, 6') 0.25, (3, 3', 7, 7') 0.3, and (4, 4', 8, 8') 0 V. The inset shows the spe- Status Solidi A 66, 779 (1981). ciﬁc features in the dependences ε'(T) measured during (1'Ð 3. E. P. Svirina, Izv. Akad. Nauk SSSR, Ser. Fiz. 34 (6), 3') cooling. Curve 3 in the inset is depicted for comparison. 1162 (1970). 4. Sh. Sh. Bashkirov, A. D. Liberman, V. V. Parfenov, and V. I. Sinyavskiœ, Izv. Akad. Nauk SSSR, Neorg. Mater. dences shown in Fig. 1, for which Utest is also equal to 15 (3), 516 (1979). 56 mV). 5. F. K. Lotgering, J. Phys. Chem. Solids 25 (1), 95 (1964). Figure 3 shows the dependences ε'(T) and ε''(T) 6. V. P. Miroshkin, Ya. I. Panova, and T. V. Stakhieva, Phys. measured at a low test-signal voltage Utest and dc polar- Status Solidi A 66, 503 (1981). izing voltage Up = 0Ð0.3 V in the course of heating and 7. A. V. Ramana Reddy, G. Ranga Mohan, D. Ravinder, cooling. The measurements were performed with a and B. S. Boyanov, J. Mater. Sci. 34, 3169 (1999). temperature step of 2 K. Actually, these dependences at 8. G. Ranga Mohan, D. Ravinder, A. V. Ramana Reddy, and ≠ B. S. Boyanov, Mater. Lett. 40, 39 (1999). Up 0 exhibit a pronounced temperature hysteresis. Analysis of the dependences ε'(T) and ε''(T) measured 9. Radha and D. Ravinder, Indian J. Pure Appl. Phys. 33, 74 ≠ ε (1995). during heating at Up 0 shows that the values of ' jumpwise increase and the values of ε'' jumpwise 10. M. A. El Hiti, J. Magn. Magn. Mater. 192, 305 (1999). decrease in the same temperature range 460Ð530 K. 11. M. E. Lines and A. M. Glass, Principles and Applica- The drastic changes observed in the dielectric charac- tions of Ferroelectrics and Related Materials (Oxford Univ. Press, Oxford, 1977; Mir, Moscow, 1981). teristics start and end at temperatures Tstart and Tend, respectively. Note that the temperature Tend monotonically decreases with an increase in the dc polarizing Translated by O. Borovik-Romanova

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

ERRATA

Erratum: “Phase Separation of the Spin System

in the La0.93Sr0.07MnO3 Crystal” [Phys. Solid State 45 (12), 2297 (2003)] S. F. Dubunin, V. E. Arkhipov, S. G. Teploukhov, V. D. Parkhomenko, N. N. Loshkareva, and N. I. Solin

In the article of S. F. Dubunin, V. E. Arkhipov, S. G. Teploukhov, V. D. Parkhomenko, N. N. Loshkareva, and N. I. Solin, the name of the ﬁrst author should read S. F. Dubinin.

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 22Ð26. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 26Ð30. Original Russian Text Copyright © 2004 by Shteœnman, Vdovin, Izotov, Parkhomenko, Borun. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Photoluminescence and Structural Defects in Silicon Layers Implanted by Iron Ions É. A. Shteœnman*, V. I. Vdovin**, A. N. Izotov*, Yu. N. Parkhomenko***, and A. F. Borun*** * Institute of Solid-State Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia ** Institute for Chemical Problems of Microelectronics, B. Tolmachevskiœ per. 5, Moscow, 109017 Russia *** Moscow State Institute of Steel and Alloys, Leninskiœ pr. 4, Moscow, 117936 Russia

Abstract—The photoluminescence spectra of silicon samples implanted by 56Fe+ ions [energy, 170 keV; dose, 1 × 1016, (2Ð4) × 1017 cmÐ2] and annealed at temperatures of 800, 900, and 1000°C are measured. The structure of the samples at each stage of treatment is investigated using transmission electron microscopy (TEM). It is found that the phase formation and morphology of crystalline iron disilicide precipitates depend on the dose of iron ions and the annealing temperature. A comparison of the dependences of the intensity and spectral distribution of the photoluminescence on the measurement temperature, annealing temperature, and morphology of the FeSi2 phase revealed the dislocation nature of photoluminescence. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION 2. EXPERIMENTAL TECHNIQUE

β 56 + The semiconductor phase -FeSi2 is a promising Iron ions Fe with an energy of 170 keV and doses material, because it can easily be integrated with silicon of 1 × 1016 and (2Ð4) × 1017 cmÐ2 were implanted into technology and emits in the range of 0.8 eV owing to n-Si(100) wafers (KÉF-4, 5) 75 mm in diameter at a the direct-gap electronic structure with a band gap of temperature of 350°C. Thermal annealing was carried approximately 0.85 eV at room temperature [1]. How- out in an argon atmosphere at temperatures of 800Ð ° ever, practical application of this material presents con- 1000 C for 30 min. The structure of the samples was investigated by transmission electron microscopy siderable difficulties for a number of reasons. In partic- β (TEM) with the use of a JEM 200CX electron micro- ular, Lange [2] revealed that continuous layers of - scope. The TEM observations were performed on lon- FeSi2 with a high degree of structural perfection do not gitudinal foils (oriented along the wafer surface) and exhibit luminescence properties. Gumarov et al. [3] cross sections. The sizes of rounded particles and grains established that crystalline and strained states of iron in the form of polyhedra were characterized by the disilicide particles and their morphology substantially diameters of the circumscribed circles. The photolumi- depend on the conditions of ion-beam synthesis. More- nescence (PL) of the samples placed in an optical over, the luminescence properties of these particles helium cryostat was excited by an Ar laser (514.5 nm) appeared to be different. Grimaldi et al. [1] and Marti- and was then recorded on standard phase-sensitive nelli et al. [4] showed that elastically strained ball- instruments with the use of an MDR-2 wide-aperture monochromator and a cooled germanium photoresistor. shaped particles involved in a defect-free matrix do not possess luminescence properties, whereas unstrained disk-shaped particles in a matrix with a large number of 3. RESULTS defects emit with an energy of 0.8 eV. Many authors have noted that the origin of this emission is not clearly It is found that the phase formation and morphology understood, because the D1 line associated with the of crystalline iron disilicide precipitates depend on the dislocation luminescence is observed in the same spec- dose of iron ions and the annealing temperature. In the tral range. From the aforesaid, it is clear that elucidation general case, the surface region of the silicon wafer after ion-beam synthesis contains misoriented (with of the nature of the emission in this range is an impor- respect to the silicon matrix) single-crystal grains and tant problem. The purpose of the present work was to small-sized rounded particles of iron disilicide and also reveal the origin of the luminescence in the range of dislocations. The single-crystal structure of particles 0.8 eV in silicon samples containing iron disilicide pre- and grains is confirmed by the appearance of numerous cipitates formed during ion-beam synthesis and charac- extra reflections in the diffraction pattern and the moiré terized by different morphology. contrast in the electron microscope images.

PHOTOLUMINESCENCE AND STRUCTURAL DEFECTS 23

3.1. Implantation with a Dose of 1 × 1016 cmÐ2 (a) 3000 The photoluminescence spectrum of the implanted Sample 1 P = 2 W/cm2, 514 nm sample exhibits only exciton luminescence of silicon exc due to the excitation of the undistorted layer of the sub- 2000 4.2 K strate. In the photoluminescence spectrum of the sam- 50 K ple annealed at 800°C (sample 1), the broad band with 1000 a maximum at 0.807 eV is dominant (Fig. 1a). The 0 position of this maximum exactly coincides with that of (b) the dislocation photoluminescence line D1. An increase in the sample temperature to 50 K leads to a decrease in 1000 Sample 2 4.2 K the intensity of the band. Note that the degree of quenching of the long-wavelength wing is considerably PL intensity, arb. units smaller than that of the other portion of the band. Such a behavior of the photoluminescence band indicates 0 0.8 0.9 1.0 1.1 that the emitting centers responsible for this lumines- Energy, eV cence have different natures. The TEM investigations of sample 1 revealed that the surface region of the wafer contains rounded parti- Fig. 1. Photoluminescence spectra of the samples implanted with an iron ion dose of 1 × 1016 cmÐ2 and annealed at tem- cles and dislocations (Fig. 2). The particle sizes vary ° from 3 to 30 nm, and the density of particles exceeds peratures of (a) 800 and (b) 900 C. 8 × 1010 cmÐ2. The dislocation density can be approximately estimated at >1010 cmÐ2. The moiré contrast fringes of different particles are considerably misoriented. This suggests that particles are irregularly arranged in the silicon matrix. The diffraction pattern exhibits a relatively small number of extra reflections, which are predominantly located within the fringe passing through the {220} main reflections. These extra reflections precisely correspond to the reflections from β the (114), (422), and (313) planes of the -FeSi2 phase. The other few weak extra reflections coincide with fringes for the (040), (204), and (222) reflections of the β -FeSi2 phase. In the photoluminescence spectrum of the sample annealed at 900°C (sample 2), the D1 line is also dominant, even though the intensity of this line decreases compared to that for sample 1 and the other lines D2Ð (a) 100 nm D4 of the dislocation luminescence are clearly observed in the spectrum (Fig. 1b). It should be noted that the exciton photoluminescence is characterized by a rather high intensity.

3.2. Implantation with a Dose of 2 × 1017 cmÐ2 The sample implanted with a dose of 2 × 1017 cmÐ2 (like the sample implanted at a lower dose and annealed at 800°C) involves particles and dislocations. The difference lies in the increase in the density (≥2 × 1011 cmÐ2) and the sizes (20Ð50 nm) of particles. The diffraction pattern contains a large number of extra reflections, among which there are very intense reflections with a regular arrangement. This indicates that the total vol- (b) 100 nm ume of iron disilicide particles increases and they are more regularly oriented in the Si matrix. For the most part, the particles are characterized by the reflections Fig. 2. TEM dark-field images of the sample implanted with β from the (114) planes of the -FeSi2 phase. Moreover, an iron ion dose of 1 × 1016 cmÐ2 and annealed at a temper- ° β a regular arrangement is observed for the reflections ature of 800 C: (a) -FeSi2 particles (extra reflection) and β 〈 〉 from the (202) and (224) planes of the -FeSi2 phase. (b) dislocations ( 220 main reflection).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

24 SHTEŒNMAN et al. number of grains emerge on the surface. Other grains are covered with a relatively thick silicon layer containing particles. The three-dimensional dislocation network has a cellular structure and extends from the lower boundary of the iron disilicide layer into silicon to a depth of 400 nm. The diffraction pattern exhibits numerous extra reflections coinciding with those char- β acteristic of the -FeSi2 phase. Isolated particles and individual grains are simultaneously observed in the dark-field images in extra reflections, which suggests their identical crystal structure. The photoluminescence spectrum of this sample exhibits an intense band at 100 nm 0.807 eV (Fig. 4). Annealing of the initial implanted sample at 1000°C leads to the formation of a discontinuous layer that has Fig. 3. TEM image of the sample implanted with an iron ion a similar shape but consists of large-sized single-crystal dose of 2 × 1017 cmÐ2 and annealed at a temperature of fragments. The density of rounded particles is substan- 900°C (〈220〉 main reflection). tially lower, and the dislocation structure remains almost unchanged. The diffraction pattern contains reg- α ularly arranged extra reflections typical of the -FeSi2 phase. No photoluminescence peak is observed in the range 0.7Ð1.1 eV in the spectrum of this sample (Fig. 4).

900°C 17 Ð2 1000°C 3.3. Implantation with a Dose of 4 × 10 cm At an implantation dose of 4 × 1017 cmÐ2, we also studied samples of three types, including the initial implanted sample and the samples annealed at 900 and 1000°C. The fundamental difference between these materials and those implanted with a dose of 2 × PL intensity, arb. units 1017 cmÐ2 resides in the fact that the continuous layer of iron disilicide in the former materials is formed even at 0.8 0.9 1.0 1.1 the implantation stage. The other structural features of Energy, eV the materials remain approximately the same, including β α the formation of the -FeSi2 and -FeSi2 phases at the Fig. 4. Photoluminescence spectra of the samples implanted corresponding annealing temperatures. These materials with an iron ion dose of 2 × 1017 cmÐ2 and annealed at tem- (irrespective of the type of iron disilicide phase) are peratures of 900 and 1000°C. characterized by a complete absence of photoluminescence in the spectral range under study. In general, all the extra reﬂections observed in the diffraction pattern coincide with those typical of the β- 4. DISCUSSION FeSi phase. The photoluminescence spectrum of this 2 The results obtained demonstrate that the β-FeSi sample does not involve the band at 0.8 eV, even though 2 it contains iron disilicide particles and dislocations. phase crystallizes during implantation of iron ions into silicon at a temperature of 350°C. The misorientation of Annealing of this sample at 900°C (sample 3) moiré fringes of the particles and the presence of a large results in the formation of a discontinuous layer com- number of irregularly arranged extra reﬂections in the posed of strongly misoriented grains with sizes from diffraction pattern indicate that particles are randomly 0.1 to 0.7 µm (Fig. 3). Rounded particles 10Ð55 nm in distributed over the silicon matrix. A similar distribu- β size are observed against the background of grains and tion of -FeSi2 particles was observed by Grimaldi open regions. The density of particles is nonuniform et al. [1] in the case when the implantation of iron ions and reaches a maximum on open regions (approxi- was performed into a preliminarily amorphized silicon mately 2 × 1010 cmÐ2). A homogeneous dense disloca- layer and was accompanied by solid-phase epitaxy at a tion network extends over the entire surface of the sam- temperature of 600°C followed by annealing at 800°C ple. Examination of the cross section of the sample for 20 h. A comparison of these data allows us to revealed that grains are predominantly planar in shape; assume that, in our samples, the implantation is however, their thickness varies from 100 to 200 nm. A attended by the amorphization of the surface silicon

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 PHOTOLUMINESCENCE AND STRUCTURAL DEFECTS 25 layer and its recrystallization due to in situ annealing. It For the majority of samples studied, the photolumi- should be noted that this assumption is not consistent nescence spectra do not exhibit bands in the energy with the data obtained in [1], according to which the range 0.75Ð1.1 eV, which is explained by different fac- heating of the sample to 250Ð300°C in the course of tors. First, these bands are absent in the spectra of all implantation suppresses amorphization of the material. the initial implanted samples (in situ annealed at a tem- However, it is obvious that the β-FeSi phase crystal- perature below 800°C) regardless of the dislocation 2 β lizes upon in situ annealing at a temperature consider- density and the morphology of the -FeSi2 phase (iso- ably below 800°C. The phase is formed through succes- lated particles, discontinuous layer, continuous layer). sive stages of nucleation of isolated particles and The possible reason for the absence of the lumines- growth of large-sized particles to grains in the form of cence in these samples is the high density of nonradia- polyhedra with a pronounced crystallographic faceting. tive-recombination centers due to the generation of Nucleated particles are distributed throughout the depth point defects in the course of implantation. Further- of the implanted layer. In turn, grains are predomi- more, the photoluminescence bands are not observed in nantly formed from particles in the layer bulk, grow, the spectra of all samples containing the continuous and emerge on the wafer surface. layer of iron disilicide irrespective of the type of phase: β ° α ° -FeSi2 (900 C) or -FeSi2 (1000 C). It seems likely The dislocation structure is formed concurrently α that the metallic conductivity inherent in the -FeSi2 with the formation of particles in the course of in situ phase is responsible for the absence of luminescence in annealing upon implantation. The mechanism of pris- α the -FeSi2 samples with continuous and discontinuous matic slip of dislocation loops under the action of crys- layers. It is known that the presence of metallic precip- tallized particles is ruled out, because the volume per β itates leads to a drastic decrease in the lifetime [7, 8] atom in the orthorhombic lattice of the -FeSi2 phase and, as a consequence, to complete quenching of pho- (12.5 Å) is smaller than that of silicon (20.0 Å). More- β toluminescence. In the case of the -FeSi2 phase, the over, it is clearly seen that the dislocation loop arrange- reason for the absence of the luminescence in the sam- ment characteristic of this mechanism is absent in the × 17 Ð2 ple with a continuous layer (DFe = 4 10 cm ) TEM images. Most likely, the dislocation structure in remains unclear. As regards the dislocation photolumi- the form of the dense three-dimensional network arises nescence lines in the spectrum of the same sample, we from the crossing of numerous V-shaped dislocations can suggest at least two possible reasons for their generated in a transition region between amorphous and absence. The ﬁrst reason is associated with the radia- crystalline silicon during the solid-phase epitaxy [5]. tion-induced defects: the concentration of these defects An analysis of the experimental data shows that at large doses can prove too high to ensure their anneal- there is a clear correlation between the luminescence of ing in 30 min. The second reason is the absorption of the material in the range of 0.8 eV and the structural the main portion of exciting radiation in the layer of features of the silicon layer prepared by ion-beam syn- iron disilicide whose band gap is narrower than the thesis. The intense luminescence at 0.8 eV is observed band gap of silicon. The absence of exciton photolumi- only for samples 1Ð3 with a high density of particles nescence from the substrate layer below the boundary and dislocations. As was noted above, the photolumi- of penetration of iron ions conﬁrms the profound effect × 16 Ð2 of defects formed in the course of implantation. nescence spectrum of sample 1 (DFe = 1 10 cm , 800°C) exhibits a band with the features characteristic The above inferences regarding the dependence of of the photoluminescence line D1. The data on the tem- the quantum yield of photoluminescence on structural perature quenching of this band demonstrate that it is a defects refer primarily to the silicon matrix and radia- superposition of lines of different natures. The above tive-recombination centers in it and, to a considerably β behavior of the photoluminescence intensity counts in lesser extent, to particles of the -FeSi2 phase. Actually, favor of the dislocation origin of this band, because the apart from the excitation transfer from the silicon temperature behavior of the intensity of the photolumi- matrix to iron disilicide particles (whose mechanism nescence in the β-FeSi phase does not depend on the still remains unknown), there exists a direct excitation 2 β wavelength [4]. The long-wavelength wing of the dislo- of the -FeSi2 phase due to absorption of the exciting β cation photoluminescence band is attributed to the laser radiation. Therefore, if we assume that the -FeSi2 recombination at dislocationÐimpurity complexes. In phase is at least partially responsible for the photolumi- particular, as was established earlier in [6], dislocationÐ nescence, it is hard to explain the absence of lumines- β oxygen complexes make a contribution to this luminescence from the continuous layer of the -FeSi2 phase cence and the thermal stability of the long-wavelength (see the data for the sample implanted with a dose of 4 × wing is higher than that of the lines D1 and D2 owing 1017 cmÐ2). A serious argument in support of the dislo- to the higher ionization energy at the upper level. The cation nature of the observed luminescence is provided short-wavelength wing of the photoluminescence band by the intensity distribution in the photoluminescence is also associated with dislocation and arises upon the spectra of samples 1 and 2, which were implanted with formation of oxygen precipitates in the samples with the same ion dose but were annealed at different tem- dislocations. peratures. The half-width of the dominant lumines-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 26 SHTEŒNMAN et al. cence band of the sample annealed at 900°C is approx- temperature below 800°C) and annealed samples with imately 10 meV less than that of the sample annealed at a continuous layer of iron disilicide. Intense lumines- 800°C. This is characteristic of the D1 line in the case cence was observed only in the samples with a high β of rapid cooling of the sample after annealing and is density of -FeSi2 particles and dislocations. These associated with the partial depinning of dislocations samples were prepared at iron ion doses of ≤2 × 1017 from oxygen precipitates. Moreover, the spectrum of cmÐ2 and annealing temperatures of 800Ð900°C. It was sample 2 exhibits other lines of the dislocation photolu- established that, in these materials, dislocations and minescence, which also confirms the dislocation origin their complexes with oxygen are primarily responsible × 17 Ð2 of the entire spectrum. Sample 3 (DFe = 2 10 cm , for the luminescence in the range of 0.8 eV. 900°C) contains similar structural elements and also β the -FeSi2 polycrystalline discontinuous layer, which covers approximately 50% of the sample surface. It is ACKNOWLEDGMENTS interesting to note that the shape of the dominant band This work was supported in part by the International in the spectra of samples 1 and 3 turns out to be virtu- Association of Assistance for the promotion of cooper- ally identical, whereas the intensity of this band for ation with scientists from the New Independent States sample 3 is approximately 40% lower than the intensity of the former Soviet Union, project INTAS no. 2001- of the band for sample 1. This can be explained by the 0194. fact that a considerable part of the dislocation network β is shielded by the -FeSi2 polycrystalline layer. Other- wise (under the assumption that this band is assigned to REFERENCES β the -FeSi2 phase), the band intensity should increase 1. M. G. Grimaldi, C. Bongiorno, C. Spinella, et al., Phys. as a result of a substantial increase in the phase volume Rev. B 66, 085319 (2002). in sample 3. Moreover, the same discontinuous layer 2. H. Lange, Phys. Status Solidi B 201, 3 (1997). β does not shield -FeSi2 particles, because, in the silicon 3. G. G. Gumarov, V. Yu. Petukhov, V. A. Shustov, and matrix, they are located above grains that do not emerge I. B. Khaibullin, Nucl. Instrum. Methods Phys. Res. B on the surface. These findings indirectly confirm the 127Ð128, 321 (1997). dislocation nature of the luminescence under investiga- 4. L. Martinelli, E. Grilli, D. B. Migas, et al., Phys. Rev. B tion. 66, 085320 (2002). 5. V. I. Vdovin, A. K. Gutakovskiœ, Yu. A. Nikolaev, and M. G. Mil’vidskiœ, Izv. Akad. Nauk, Ser. Fiz. 65 (2), 281 5. CONCLUSIONS (2001). Thus, we investigated the formation of iron disili- 6. E. A. Steinman and H. G. Grimmeiss, Semicond. Sci. cide phases and elucidated the influence of the struc- Technol. 13, 124 (1998). tural features on the photoluminescence in silicon lay- 7. A. Cavallini, M. Vandini, F. Corticelli, et al., Inst. Phys. ers implanted by iron ions. It was found that there is a Conf. Ser. 134 (3), 115 (1993). correlation between the luminescence of the material in 8. V. Kveder, M. Kittler, and W. Schröter, Phys. Rev. B 63, the range of 0.8 eV and the structural features of the sil- 115208 (2001). icon layer prepared by ion-beam synthesis. This luminescence was not revealed in the photoluminescence spectra of as-implanted samples (in situ annealed at a Translated by O. Borovik-Romanova

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 27Ð31. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 31Ð34. Original Russian Text Copyright © 2004 by Belyakov, Burdov, Gaponova, Mikhaylov, Tetelbaum, Trushin.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Phonon-Assisted Radiative ElectronÐHole Recombination in Silicon Quantum Dots V. A. Belyakov*, V. A. Burdov*, D. M. Gaponova**, A. N. Mikhaylov*, D. I. Tetelbaum*, and S. A. Trushin* * Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950 Russia ** Institute of the Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected]

Abstract—The temperature dependence of the photoluminescence (PL) spectrum of silicon quantum dots (QDs) is studied both theoretically and experimentally, and the time of the corresponding electronÐhole radiative recombination is calculated. The dependence of the recombination time on the QD size is discussed. The experiment shows that the PL intensity decreases by approximately 60% as the temperature increases from 77 to 293 K. The calculated characteristic recombination time has only a weak temperature dependence; therefore, the decrease in the PL intensity is associated primarily with nonradiative transitions. It is also shown that the phonon-assisted radiation is much more efﬁcient than the zero-phonon emission. Moreover, the zero- phonon recombination time depends on the QD radius R as R8, whereas the phonon-assisted recombination time depends on this radius as R3. © 2004 MAIK “Nauka/Interperiodica”.

In the past decade, considerable attention has been authors, which appears to be due to differences in the given to the investigation of nanostructures containing nanocrystal formation and experimental conditions. silicon quantum dots (QDs). This interest is associated, In this paper, we study the PL spectra and the times in particular, with the ability of Si nanocrystals to emit of the electronÐhole recombination for the nc-Si : SiO electromagnetic energy efficiently at room tempera- 2 ture. The experimentally obtained photoluminescence system produced through implantation of Si ions fol- (PL) spectra have a peak at energies from 1.4 to 1.8 eV, lowed by annealing. SiO2 layers were thermally grown depending on the QD size. In this case, the photolumi- on a Si substrate in the “dry–wet–dry” cycle. Then, they were irradiated with Si+ ions (150 keV, 1017 cmÐ2) and nescence itself is associated either with direct electronÐ ° hole interband recombination or with interband transi- annealed in a dry nitrogen flow at 1000 C for two hours. The photoluminescence was excited by an Ar tions involving the interface states. Along with the radi- λ ative transitions, nonradiative transitions (for example, laser ( = 488 nm). The PL spectra were measured at Auger processes) take place in the quantum dots. For 293 and 77 K. It can be seen from Fig. 1 that the lumi- this reason, the PL intensity, proportional to the quan- nescence peak at ~1.6 eV (usually associated with the tum efficiency of the photon generation, is usually Si nanocrystals) observed at 77 K is about 1.6 times determined by the following formula (see, e.g., [1]): higher than that at 293 K. τ According to Eq. (1), the PL intensity does not ∝ nr depend on temperature in the case of τ Ӷ τ . Thus, the I ------τ τ-, (1) r nr nr + r difference between the experimentally obtained inten- τ Ӷ where τ and τ are the characteristic times of the radi- sities at 77 and 293 K indicates that the condition r r nr τ ative and nonradiative transitions, respectively. Equa- nr is not satisfied in the range 77 K < T < 293 K. Hence, τ τ tion (1) determines the photoluminescence as a func- either r and nr are of the same order of magnitude or tion of temperature and of the nanocrystal size. There- the probability of the nonradiative transitions is much τ τ fore, it is necessary to know both r and nr. larger than the probability of the radiative transitions. The dependence of the photoluminescence on tem- In order to clarify the question, theoretical analysis perature and QD size has been the subject of many is required. For this purpose, we analytically calculated experimental studies (see, e.g., [1Ð7]). Most of these the probability of radiative interband recombination in papers reported a negligible temperature dependence of a quantum dot. It was shown in [8, 9] that, although the the photoluminescence; namely, the PL intensity probability of the conduction-to-valence band electron observed at room temperature was only 2Ð3 times transition with single-photon emission is nonzero, it is smaller than that at 10 K. However, there is some scat- fairly small (only ~103 sÐ1 for a 4-nm quantum dot) in ter in the experimental results obtained by different comparison with the probability of nonradiative transi-

28 BELYAKOV et al.

2500 1—77 K respectively, and the operators Wˆ and Uˆ are given by 2—293 K 1 the relationships 1–77 K 2000 πប 2 2–293 K 2 e + Wˆ = ∑ ------()cˆ , σ + cˆ , σ ()e , σpˆ , (3) 2ω () k k k k, σ m0 σ k V 1500 2 ˆ ( (), γ + ˆ U = Ð∑∑ Snm q aˆ n aˆ mbq, γ 1000 q, γ nm, (4) + +

PL intensity, arb. units (), γ ˆ ) + Snm Ðq aˆ n aˆ mbq, γ . 500 + + ˆ + ˆ Here, cˆ k, σ (cˆ k, σ ), aˆ k, σ (aˆ k, σ ), and bk, σ (bk, σ ) are the creation (annihilation) operators of photons, electrons, 0 1.2 1.4 1.6 1.8 and phonons, respectively; Ðe and m0 are the charge and Photon energy, eV mass of a free electron; pˆ is the electron momentum operator; and V is the volume of a photon resonator. γ + The quantity Snm(q, ) is determined by Fig. 1. PL spectrum of SiO2 layers irradiated with Si ions. Radiation dose 1017 cmÐ2. The samples were annealed at S ()q, γ 1000°C for two hours. nm ប (5) Ψ Ψ ()∇() = eq, γ ------∫dr n* m exp i qr U0, 2MNνγ ()q tions. In what follows, it is shown that the phonon- assisted radiative transitions (in which single-photon where M is the mass of a Si atom, N is the number of Ψ emission is accompanied by the emission or absorption unit cells in the nanocrystal, m is the electron wave of at least one phonon) are much more probable. function in state m, and U0 is the lattice potential. The vectors ek, σ and eq, γ define the direction of oscillations Let us consider a Si nanocrystal (QD) of radius R of the electric field and the atoms in the crystal lattice, implanted into an amorphous SiO2 layer, and let us respectively. assume that the QD electron subsystem interacts with The initial state corresponds to an electronÐhole pair the electromagnetic field and vibrations of the crystal being in the ground state and an ensemble of photons lattice. The total phonon-assisted electronÐhole recom- and phonons, whose distribution over k, σ and q, γ is bination rate, equal to the reciprocal of the radiative described by the Bose–Einstein statistics. In the final transition time, is determined in the second-order per- state, the valence band is completely occupied and the turbation theory as conduction band is empty. The number of photons in the final state always increases by one, whereas the 2 number of phonons is either larger or smaller by one π τ Ð1 2 WiaUaf + UiaWaf than that in the initial state. cv = ------ប ∑∑ ∑------ε ε - a Ð i k, σ q, γ a (2) In order to find the electron wave functions in the envelope-function approximation, we must solve the ×δ[ ()E ++បωσ()k បνγ ()q Ð E f e equation + δ()]E + បωσ()k Ð បνγ ()q Ð E . f e ˆ () () HijF j r = EFi r . (6) Here, the matrix elements of the electronÐphoton (Wˆ ) ˆ Here, Hij is a matrix differential operator, Fj(r) is the and electronÐphonon (Uˆ ) interaction operators are cal- envelope function, and E is the energy. In the absence culated between the initial i (or the final f) and an inter- of spinÐorbit interaction (which is weak in silicon), the mediate state a; Eh and Ee are the energies at the valence operator Hˆ ij in the valence band is the following 3 × 3 band top and the conduction band bottom, respectively matrix [10]: (below, these energies are determined by solving the 2 ε ε () ប Schrödinger equation); and a and i are the total ener- ˆ h δ ˆ LMÐ ()ˆ 2 ˆ 2 Hij = ijH0h + ------k Ð 3k j gies of the intermediate and initial states, respectively, 2m0 3 including not only the energies of the electrons but also (7) ប2 the energies of the photons and phonons. The photon ()δ ˆ ˆ + ij Ð 1 ------Nkik j, and phonon frequencies are denoted as ωσ(k) and νγ(q), 2m0

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 PHONON-ASSISTED RADIATIVE ELECTRONÐHOLE RECOMBINATION 29 where L, M, and N are equal to 6.8, 4.43, and 8.61, This function can be found as the solution of the Schrödinger equation with the isotropic Hamiltonian (8) respectively [11], and Hˆ 0h is the isotropic operator obtained by averaging the Hamiltonian (7) over the corresponding to its ground state. angles Without considering the spin, the lowest level in the conduction band is sixfold degenerate and has the 2 ប 2 energy Hˆ = Ð------kˆ . (8) 0h 2m h ()2 E0 + E1 Ð Q E1 Ð E0 Ð Q 2 E = ∆ Γ + ------Ð ------+,J (13) Here, mh = 3m0/(L + 2M) is the isotropic effective hole e X 2 4 mass, equal to 0.19m0. The wave vector and the energy are measured from their values at the Γ point. where E0 and E1 are the energies of the s and p states of the isotropic Hamiltonian (10) and are equal to In the conduction band, the Hamiltonian Hˆ should ij ប2π2/2m R2 and ប2µ2/2m R2, respectively. Here, µ is the be written as a 2 × 2 matrix in the vicinity of one of the e e three physically nonequivalent X points of the Brillouin first root of the equation xcosx = sinx and the quantities zone [12]. In the [001] direction, for example, the J and Q are matrix elements of the Hamiltonian are given by ប2 2 2 k0 2πµ ប 2µ 1 1 J ==------, Q ------Ð ----- . 2 2 2 2 2  ()e ()e ប iប k µ π 15 mt ml ˆ ˆ ˆ 1 1 ˆ ˆ 0 ˆ 3ml R Ð R H11 ==H22 H0e ++----- ----- Ð ----- kxky ------kz, 6 mt ml ml (9) The corresponding wave functions can be chosen in the ប2 following form (as an example, we cite only two of the ˆ ()e ()ˆ ()e + ប21 1 ˆ ˆ i k0 ˆ six wave functions corresponding to the X point in the H12 ==H21 ----- Ð ------kxky + ------kz, mt m0 ml [001] direction; the other functions can be built in the same way): where the wave vector is measured from the X point; Ψ ()λ ()|〉 ()λ ()|〉 mt and ml are the transverse and longitudinal effective e1 = cos u1z r 0 + sin u2z r z , ≈ × π (14) masses, respectively; k0 0.144 2 /a0 is the distance Ψ = cos()λ u ()r |〉0 Ð sin()λ u ()r |〉z , between the X point and the nearest energy minimum in e2 2z 1z the k space; and a0 is the lattice constant. The isotropic where u1z(r) and u2z(r) are the Bloch functions of the λ averaged Hamiltonian Hˆ 0e is bulk crystal at the X point and the parameter is determined by the relationships ប2 ˆ ∆ ˆ 2 E Ð E Ð Q H0e = XΓ + ------k , (10) λ 1 0 2me cos2 = ------, ()2 2 E1 Ð E0 Ð Q + 4J where me = 3mlmt/(2ml + mt) is the isotropic effective ∆ electron mass and XΓ = 1.215 eV [12] is the energy dif- 2J ference between the conduction band at the X point and sin2λ = ------. Γ ()2 2 the valence band at the point. E1 Ð E0 Ð Q + 4J Equation (6) was solved in [13] in the approximation of infinitely high barriers by using the operators It should be noted that an attempt to calculate the prob- given by Eqs. (7)Ð(10). This made it possible to find the ability of the interband phonon-assisted transition has wave functions and energies of the ground states of the already been made [14]. However, the calculation of the electrons and holes (they are assumed to be known envelope functions and electronic energies in that paper below). The ground-state energy in the valence band is was in error and gave rise to recombination times that were overestimated by more than order of magnitude in ប2π2 comparison with our results. ------Eh = Ð 2. (11) The reciprocal time of the phonon-assisted elec- 2mh R tronÐhole recombination calculated from Eq. (2) using This level remains triply degenerate (the spin is not taken wave functions (12) and (14) is into account); the corresponding wave functions are Λ 2ε3/2ប 2 2 λ 3 ()បν τ Ð1 e k0 cos a0 coth /2kBT Ψ ()|〉 Ψ ()|〉 cv = ------------, (15) h1 ==v x r 0 , h2 v y r 0 , π2 2 3 R ν (12) 24 ml Mc ()Ee Ð Eh Ψ ()|〉 h3 = v z r 0 , where a0 = 0.543 nm is the silicon lattice constant, kB is where vx(r), vy(r), and vz(r) are the Bloch functions of Boltzmann’s constant, T is the temperature, ε ≈ 12 is the the bulk crystal at the Γ point and |0〉 is the s-type enve- dielectric constant, ν is the frequency of transverse lope function, which is the same for these three states. optical (TO) phonons at the Brillouin zone boundary at

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 30 BELYAKOV et al.

7 according to [14, 15], the intensity of their interaction with electrons is one and two orders of magnitude smaller, respectively, than that for TO phonons. Assum- 293 K 293 K ing that the QD ﬁnite size cannot change the results drastically, we took into account only the TO-phonon 77 K 5 77 K contribution in Eq. (15). ]

–1 For the reciprocal of the zero-phonon radiative elec- [s tronÐhole recombination time, we have –1 –1 τ 2 3/2 2 log ε ()8 τ Ð1 e P Ee Ð Eh a0 ( 2 ()λ 2 ()π 3 0 = ----------- cos cos 2 R/a 12π4m 2ប2c3 R 0 (17) +3µ2/π2 sin2 ()λ sin2 ()2πR/a ),

1 where the parameter P is determined by the Fourier 1.0 1.52.0 2.5 3.0 amplitudes of the Bloch functions; its value is close to , nm R (Ps)ij. A comparison of Eqs. (15) and (17) reveals two important differences between the phonon-assisted and Fig. 2. The probability of electronÐhole recombination as a zero-phonon radiative transitions. function of the QD radius. The upper curves correspond to First, the recombination time for phonon-assisted phonon-assisted transitions, and the lower curve, to zero- phonon transitions. transitions depends on the QD size much more weakly than that for zero-phonon transitions, namely, as R3 instead of R8. Thus, we have τ Ð1 ӷ τ Ð1 and this ine- the X point (បν ≈ 57.5 meV [15]), and the parameter Λ cv 0 determines the intensity of the electronÐphonon inter- quality becomes much more stronger as the QD size R action and is equal to grows (see Fig. 2). Second, the recombination time corresponding to phonon-assisted transitions depends 2 3 π (though only weakly) on the temperature (Fig. 2); Λ 53 2 () namely, as the temperature increases from 77 to 293 K, = ------∑ ∑ ∑ ------PzPs ij -- 6 m0a0 the time τ decreases by approximately 20Ð25%. i = 1 j = 1 sxy= , cv (16) Since the inequality τ Ӷ τ is satisfied in a wide ប2 π 2 ()P 2 cv 0 2 ∆ s ij range of QD sizes (R ≥ 1 nm), it is obvious that the + ------------Ð XΓ ------ប . 2m0 a0 phonon-assisted photoluminescence is typical of QDs. Therefore, in Eq. (1), which determines the quantum τ The numerical coefficient 53 is a result of integration efficiency and PL intensity, the recombination time r τ τ over phonon wave vectors in Eq. (2), and 1/6 of the should be replaced by cv rather than by 0. According double sum over i and j is the average over all the pos- to Eq. (1), the observed 1.6 times decrease in the PL sible degenerate initial and final states. The matrix ele- intensity can be achieved only if the nonradiative tran- τ ments are determined by the formula sition time nr diminishes even more drastically. This means that the nonradiative transitions make the main contribution to the electronÐhole recombination. 1 ()ˆ () Bij = ------∫ drui* r Bv j r , V 0 V0 ACKNOWLEDGMENTS where integration is performed over the unit cell vol- This work was supported by the program “Universi- 3 ties of Russia” (project no. UR.01.01.057). ume V0 = a0 /4 and the functions vj(r) are defined by Eq. (12). The functions ui(r) are the periodical parts of the corresponding Bloch function at the X point and dif- REFERENCES fer from the functions uiz(r) in Eq. (14) by the absence 1. S. Takeoka, M. Fujii, and S. Hayashi, Phys. Rev. B 62 of the exponential factor. In the further numerical esti- (24), 16820 (2000). mates, it is assumed that both terms under the absolute- 2. Y. Kanemitsu and S. Okamoto, Phys. Rev. B 56 (24), value sign in Eq. (16) are equal to each other and 15561 (1997). ()2 3. Y. Kanemitsu, Phys. Rev. B 53 (20), 13515 (1996). Ps /2m0 = (4/3) eV for any value of i and j [14]. ij 4. Y. Kanemitsu, N. Shimizu, T. Komoda, et al., Phys. Rev. It should also be noted that not only TO phonons but B 54 (20), 14329 (1996). also longitudinal optical and transverse acoustic 5. T. Shimizu-Iwayama, S. Nakao, and K. Saitoh, Appl. phonons are excited in the bulk silicon. However, Phys. Lett. 65 (14), 1814 (1994).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 PHONON-ASSISTED RADIATIVE ELECTRONÐHOLE RECOMBINATION 31

6. G. A. Kachurin, I. E. Tischenko, K. S. Zhuravlev, et al., 11. M. Voos, Ph. Uzan, C. Delalande, et al., Appl. Phys. Lett. Nucl. Instrum. Methods Phys. Res. B 122, 571 (1997). 61 (10), 1213 (1992). 7. D. I. Tetelbaum, S. A. Trushin, V. A. Burdov, et al., Nucl. 12. A. A. Kopylov, Fiz. Tekh. Poluprovodn. (Leningrad) 16 Instrum. Methods Phys. Res. B 174, 123 (2001). (12), 2141 (1982) [Sov. Phys. Semicond. 16, 1380 (1982)]. 8. T. Takagahara and K. Takeda, Phys. Rev. B 46 (23), 15578 (1992). 13. V. A. Burdov, Zh. Éksp. Teor. Fiz. 121 (2), 480 (2002) [JETP 94, 411 (2002)]. 9. D. I. Tetelbaum, V. A. Burdov, S. A. Trushin, and 14. M. S. Hybertsen, Phys. Rev. Lett. 72 (10), 1514 (1994). A. N. Mikhaylov, in Proceedings of 10th International Symposium on Nanostructures: Physics and Technology 15. O. J. Glembocki and F. H. Pollak, Phys. Rev. B 25 (2), (St. Petersburg, 2002), p. 206. 1193 (1982). 10. A. I. Ansel’m, Introduction to the Theory of Semicon- ductors (Nauka, Moscow, 1978). Translated by A. Poushnov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 32Ð34. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 35Ð38. Original Russian Text Copyright © 2004 by Vyatkin, Gavrilin, Gorbatov, Starkov, Sirotkin.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Formation of Two-Dimensional Photonic-Crystal Structures in Silicon for Near-Infrared Region Using Fine Focused Ion Beams A. F. Vyatkin, E. Yu. Gavrilin, Yu. B. Gorbatov, V. V. Starkov, and V. V. Sirotkin Institute of Microelectronic Technology and Ultra-High-Purity Materials, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia e-mail: [email protected]

Abstract—One of the two variants of producing two-dimensional photonic crystals in silicon is the formation of ordered macropore structures in a silicon substrate. The characteristic pore dimensions (the diameter and the wall thickness between pores) determine the wavelength range in which such a pore structure exhibits the properties of a photonic crystal. For the near-infrared region, these dimensions approach 1 µm or fall in a submicron region. An ordered structure of macropores with such dimensions is formed in this work using ﬁne focused ion beams to provide the stimulating effect of implanted ions on pore nucleation in given sites on the silicon substrate surface. Pores are shown to nucleate at sites subjected to ion irradiation even at a low implantation dose (2 × 1013 ion/cm2). A model describing the orienting effect of ion irradiation on pore nucleation is proposed. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION problem of formation of photonic crystals for the near- As elements for micro- and nanophotonics, photo- infrared region. nic crystals are very promising materials, especially in the near-infrared region, used in modern communica- 2. EXPERIMENTAL tion equipment. Silicon-based photonic crystals are important in this connection, since the use of silicon We showed earlier [3] that the anodic etching of sil- and its highly developed microelectronic technology icon is a two-stage process consisting of pore nucle- makes it possible to realize integrated solutions for ation and growth stages. The pore growth rate is speci- which both microelectronic and optical schemes can be fied by the parameters of anodic etching, such as the arranged on one chip. current density, voltage, electrolyte composition, and Two-dimensional photonic crystals in silicon are temperature, whereas the density of nucleating pores is ordered structures of macropores on a silicon substrate. determined by processes that are still unclear. In this The characteristic pore dimensions (the diameter and work, we created an ordered structure of implanted the wall thickness between pores) determine the oper- sites on the silicon surface with fine focused ion beams. ating wavelength range of such a porous structure. For Then, such an irradiated silicon wafer was subjected to the near-infrared region, these dimensions approach deep anodic etching. one micrometer or fall in a submicron region [1]. It is For experiments, we used (100) p-Si wafers with a difficult to form ordered macroporous silicon with such resistivity of 5Ð8 Ω cm. The energy of singly charged pore dimensions by the methods used at present to pro- gallium ions was 25 keV. The diameter of an ion beam duce macroporous silicon having pores with a high on the sample surface was 100 nm, and the current den- aspect ratio, namely, plasmochemical etching through sity was about 1 A/cm2. The structures were exposed to masks and electrochemical deep anodic etching. It is an ion beam moving across the sample surface with the also known that, for example, irradiation of the n-Si PROXY computer program. The exposure dose was surface with boron ions terminates anodic etching in determined by the exposure time of the beam at a point irradiated sites [2] and this was attributed to the inver- and was varied from 2 × 1013 to 6 × 1014 cmÐ2. The max- sion of the conduction type in these zones. imum dose was chosen to ensure minimum sputtering In this work, we try to find a new solution to this of the surface at irradiated sites (the maximum thick- complex problem by using fine focused ion beams to ness of a sputtered layer at a dose of 6 × 1014 cmÐ2 was favor the stimulating effect of implanted ions on pore calculated to be smaller than 0.5 nm). The minimum nucleation in given sites on the silicon substrate sur- dose (2 × 1013 cmÐ2) was dictated by the device. The face. Since ion beams can be focused to nanoscale minimum exposure time at a point was 10 µs. The size sizes, we can expect that their application will solve the of an exposed site was 100 nm, and the center-to-center

FORMATION OF TWO-DIMENSIONAL PHOTONIC-CRYSTAL STRUCTURES 33 distance of the sites was varied from 1 to 5 µm. The process of deep anodic etching was performed at room temperature in a solution of hydroﬂuoric acid in dimethylformamide (DMF) (the volume ratio was HF : DMF = 1 : 9) at a current density of 9 mA cmÐ2. The etching depth, geometrical dimensions of pores, and interpore spacing were determined using optical and electron-microscopic images taken from ordered and disordered regions of longitudinal and transverse polished sections of samples.

3. EXPERIMENTAL RESULTS The deep anodic etching of the silicon samples preirradiated with gallium ions showed that pores nucleated only in irradiated sites. When studying the 5 µm samples irradiated to various doses and then etched, we did not find any dependence of pore formation on the irradiation dose over the whole dose range. Figure 1 Fig. 1. Optical photograph of the silicon wafer surface sub- shows an optical photograph of the sample surface with jected to deep anodic etching. arranged pores. It is seen that pores are arranged regularly with a period of 2.4 µm in the region preirradiated with a fine focused ion beam (Fig. 1, left-hand side). Beginning from a certain value of the pore center-to- center distance, an increase in this value lead to the formation of pores not only in the implanted sites but also 671.1 nm between them due to deep anodic etching. This effect is 987.9 nm called “the proximity effect” and is described in [3]. A decrease in the interpore distance to 1 µm results in a number of implanted sites falling out of the ensemble of growing pores; i.e., part of the pores with a center dis- 1.01 µm tance of 1 µm that form in the initial stage of etching 999.4 nm cease to grow upon further deep anodic etching. More- over, the center distance tends to 2.4 µm. It should be noted that a center distance of 2.4 µm is characteristic of spontaneous nonuniform deep anodic etching of a sili- Fig. 2. Scanning electron microscope image of the silicon con sample having the same resistivity (Fig. 1, right- wafer surface subjected to deep anodic etching under the hand side). conditions of spontaneous pore nucleation. However, the initiating effect of ion irradiation on pore nucleation manifests itself only if the depth of chemical reaction. Therefore, in the initial stage, etch- doping silicon with a gallium impurity exceeds a cer- ing takes place at “weak” sites in the first atomic layer, tain critical value. For implantation of 25-keV gallium e.g., at sites where doping impurities are located. The ions, the entire depth profile of the doping impurity in removal of an atom from the first layer facilitates etch- the silicon substrate lies within ~50 nm. If the ion irra- ing of the neighboring atoms in the first layer. The pro- diation is carried out through an oxide layer ~20 nm cess proceeds in the first layer until a doping atom of thick (which means a decrease in the depth of doping), the second layer becomes uncovered. At that instant, the stimulating effect of the ion irradiation disappears etching extends to the second atomic layer. Then, the and the process of pore nucleation and growth becomes process repeats itself in the third and the following lay- spontaneous and random. ers. It is obvious that not all of the pore nucleation centers have the same rate of propagation into the crystal, 4. DISCUSSION OF THE RESULTS since the probability of meeting a doping atom in the next layer is different for each nucleating pore. For this The orienting effect of the focused ion beam on the reason, only part of the nucleating pores have a chance formation of a pore ordered structure can be interpreted to extend deep into the crystal. in terms of the following scheme of the process of electrochemical etching. It is well established that electro- This scheme of electrochemical etching allows us to chemical etching of silicon is accompanied by develop a computer model for this process. The physi- macropore formation under the conditions of a defi- cal principles forming the basis for this model are the ciency of charge carriers supplied to the site of electro- following.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

34 VYATKIN et al.

(a) (b) (c)

Fig. 3. Two-dimensional representation of three sequential stages of deep anodic etching: (a) initial stage, (b) when the etching front reaches the tenth monolayer of silicon, and (c) when the etching front reaches the 20th monolayer. Open symbols represent impurity atoms, and solid symbols are silicon atoms.

(1) Macropores form in silicon under the conditions ing another doping atom in each next layer in the direc- of a charge-carrier deficiency at the siliconÐelectrolyte tion normal to the surface is higher than a certain criti- interface; therefore, the process of etching silicon starts cal value, depending on the impurity concentration in only in preferred sites on the wafer surface. the silicon crystal. Therefore, in the case of random (2) These sites are assumed to be the sites where spontaneous pore formation on the silicon wafer sur- impurities located. face, an ensemble of undeveloped pores (craters) will arise with a small number of pores extended deep into (3) The removal of an impurity to the electrolyte solu- the silicon wafer. This behavior is observed experimen- tion (etching-out of impurities) opens up possibilities for tally on real silicon wafers subjected to anodic etching the lateral extension of silicon etching at a significant (Fig. 2). The same result is predicted by the model rate in the layer from which the impurity was removed. described above (Fig. 3). (4) Once the lateral front of silicon etching reaches a site of an impurity in the second layer, the etching process extends immediately to this layer and proceeds 5. CONCLUSIONS laterally in it. The rate of the lateral motion of the etch- (1) We have shown that fine focused ion beams can be ing front is equal to the rate of lateral etching in the first used to form ordered macropore structures in silicon. layer until a two-atom step forms. The rate of lateral (2) We have proposed a model that describes the ini- etching of a two-atom step is taken to be an order of tial stage of macropore formation in silicon. This model magnitude smaller than the rate of lateral etching of a implies that implantation from a fine focused ion beam one-atom step. leads to a local increase in the impurity concentration in (5) When an impurity becomes uncovered in the an irradiated zone and, hence, to an increased probability third layer, the process of etching extends to the third of meeting a doping atom in each next layer in this zone, layer, and so on. The rate of lateral etching of a three- which provides pore growth deep into the bulk of silicon atom step and each next step is taken to be an order of at this site (according to the model proposed). magnitude smaller than that of the previous step. (3) The simulation results agree qualitatively with (6) This scenario is valid only to a certain depth of the experimental data, which lends support to the valid- etching a pore in silicon, i.e., only for the initial stage ity of the fundamental tenets of this model. of etching. Once all charge carriers supplied to the sili- conÐelectrolyte interface are concentrated at the bottom of the pores formed, the process of etching passes into REFERENCES the stage of pore growth and its parameters are speci- 1. T. F. Krauss and R. M. De La Rue, Prog. Quantum Elec- fied by other characteristics, such as the current density, tron. 23, 51 (1999). bias voltage, electrolyte composition, and the tempera- 2. E. V. Astrova and T. N. Vasunkina, Fiz. Tekh. Polupro- ture of the siliconÐelectrolyte system. vodn. (St. Petersburg) 36 (5), 593 (2002) [Semiconduc- The model proposed implies that not all of the impu- tors 36, 564 (2002)]. rity centers on the silicon wafer surface will be sources 3. A. Vyatkin, V. Starkov, V. Tzeitlin, et al., J. Electrochem. for forming pores. A pore will grow into the bulk of sil- Soc. 149 (1), G7 (2002). icon if the doping atom on the wafer surface on which the pore nucleated is such that the probability of meet- Translated by K. Shakhlevich

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 35Ð39. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 39Ð43. Original Russian Text Copyright © 2004 by Sobolev, Emel’yanov, Shek, Vdovin.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Effect of the Postimplantation-Annealing Temperature on the Properties of Silicon Light-Emitting Diodes Fabricated through Boron Ion Implantation into n-Si N. A. Sobolev*, A. M. Emel’yanov*, E. I. Shek*, and V. I. Vdovin** *Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia e-mail: [email protected] **Institute for Chemical Problems of Microelectronics, Bol’shoœ Tolmachevskiœ per. 5, Moscow, 119017 Russia

Abstract—The effect of the temperature of postimplantation annealing on the electroluminescence and the electrophysical and structural properties of light-emitting diodes fabricated by the implantation of boron ions into n-Si with a resistivity of 0.5 and 500 Ω cm is studied. All spectra contain strong electroluminescence (EL) peaks associated with band-to-band radiative transitions. An increase in the annealing temperature from 700 to 1100°C is accompanied by a monotonic increase in the quantum efﬁciency for the dominating EL peak and in the effective minority-carrier lifetime in the base of the light-emitting diodes and by the transformation of extended structural defects. Analysis of the experimental data shows that the extended structural defects formed are most likely to affect the EL properties via the formation or gettering of the radiative or nonradiative recombination centers rather than via preventing the removal of charge carriers to nonradiative recombination centers. The maximum internal quantum efﬁciency is reached after annealing at 1100°C (where extended structural defects are absent) and is estimated to be 0.4% at 300 K. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION 2. EXPERIMENTAL Luminescence in single-crystalline silicon (c-Si) The pÐn structures were formed through the implan- caused by band-to-band transitions or defects is studied tation of boron ions (energy E = 40 keV, dose D = 1 × for creating new optoelectronic devices. It was shown 1015 cmÐ2) into (100) n-Si KÉF-0.5 and KÉF-500 in [1] that efficient silicon light-emitting diodes (LEDs) wafers 370 and 410 µm thick, respectively. To create with a band-to-band spectrum could be fabricated by ohmic contact, phosphorus ions (E = 75 keV, D = 1 × using a relatively simple method of boron ion implan- 1015 cmÐ2) were implanted into the back side of the tation into n-Si followed by annealing at 1000°C. Those wafers. Isochronous 20-min postimplantation anneal- authors assumed that high quantum efficiency was ings were performed in an argon atmosphere at a tem- related to the formation of dislocation loops with a cer- perature Tann, and then the samples were furnace-cooled ° tain density and size in a thin diode-base layer adjacent to 600 C and removed from the furnace to the air. Tann to the pÐn junction. Such loops are assumed to induce was varied from 700 to 1100°C. Instead of being local stress fields that modify the band structure of a annealed in Ar, several structures were annealed at 900 crystal, thus preventing the removal of charge carriers and 1000°C in a chlorine-containing atmosphere cre- to nonradiative recombination centers and favoring ated by an oxygen flow with 1 mol % carbon tetrachlo- their intense band-to-band radiative recombination. To ride. During implantation and annealing, the Si surface confirm or refute these model concepts, it is necessary was coated with an 87-nm-thick layer of thermal SiO2. to study luminescence in c-Si having extended defects LEDs with mesalike edge contours were formed using of various density, size, and physical nature. The spec- a standard technology by depositing Al onto the front trum of extended defects that form in c-Si as a result of and back sides of the wafers. The working areas of the ion implantation and annealing can be controlled by pÐn junctions were 1.5 mm2. varying the temperature and atmosphere of postimplantation annealing. To excite EL, diodes were energized with a pulsed 32-Hz voltage at a pulse duration of 0.5Ð2.0 ms and a In this work, we study 1.0- to 1.6-µm electrolumi- current amplitude of up to 1000 mA. EL spectra were nescence (EL) and structural defects in pÐn structures recorded at 80Ð300 K using an MDR-23 monochroma- formed upon implantation of boron ions into single- tor, InGaAs photodetector, and a selective nanovoltme- crystalline n-Si wafers (having significantly different ter. The resolution of the system was 3 nm. Radiation levels of doping with phosphorus) and subsequent was collected from the surface of a pÐn junction not annealing. covered with aluminum and was sent into the entrance

36 SOBOLEV et al.

1.0 1.2 1.4 1.6 tion, onto the back side of the diodes. The radiation from the back side of a diode was collected with a lens system to be directed to the entrance window of an FD- 10 AG germanium photodiode. The external quantum Tann = 700°C η efﬁciency ext was determined by measuring the photoelectric current of the Ge photodiode with allowance for its currentÐillumination characteristic, the solid angle over which the radiation was collected, and the 80 K losses in the lens system, in the silicon (because of col- lecting the radiation from the back side of a wafer), and in the Ni coating. The diode radiation distribution over a hemisphere was assumed to be isotropic. Moreover, 300 K we assumed that the whole radiation focused on the entrance window of the photodiode, which was made of a minilens mounted into the case, was collected on the photoreceiving area. To calculate the internal quan- η η η tum efﬁciency int, we used the ratio ext / int = 0.013 [2], which was obtained theoretically for a planar light- emitting diode and for a semiconductor refractive index τ of 3.6. The effective minority-carrier lifetime p in the Tann = 900°C n base of the p+ÐnÐn+ structures was determined, by using the Lax method [3], from the lifetime of the phase of a high reverse conductance induced by the application of forward and backward current pulses to a diode. 80 K Structural defects were studied by transmission electron microscopy in the two-beam diffraction mode using foils oriented parallel to the wafer surface. Intensity, arb. units

300 K 3. RESULTS AND DISCUSSION Figures 1 and 2 show the EL spectra (measured at 80 and 300 K) of the diodes that were made on the KÉF- 500 (Fig. 1) and KÉF-0.5 (Fig. 2) wafers and annealed in an Ar atmosphere at various temperatures Tann. The current was 250 mA. For convenience, the EL intensity = 1100°C Tann is given on the logarithmic scale. The spectra at 80 K contain a strong EL peak with a maximum at a wave- 300 K length λ ≈ 1.13 µm and a weaker EL peak at λ ≈ 1.2 µm; the two peaks are mainly caused by exciton radiation with the participation of phonons [4]. Moreover, at 80 K, the EL spectra of the KÉF-500-based diodes annealed at 700 or 900°C and of the KÉF-0.5-based diodes annealed at 700°C exhibit a broad EL band at 80 K 1.2Ð1.6 µm caused by defects. Defect-induced EL also exists in the KÉF-500-based diodes annealed at 1100°C, but it extends to λ ≈ 1.4 µm. The observed spe- ciﬁc features of the appearance of centers of the defect- induced EL for the two types of diodes under study are likely due to the difference in the defect structures and 1.0 1.2 1.4 1.6 λ, µm impurity compositions of the initial Si wafers. The spectra measured at 300 K contain a strong EL Fig. 1. EL spectra of KÉF-500-based diodes annealed at peak with a maximum at λ ≈ 1.15 µm due to band-to- various temperatures Tann. band radiative transitions in silicon with the participation of phonons [4]. A broad band of defect-induced EL at 1.2Ð1.6 µm is observed only in the KÉF-500-based slit of the monochromator. To measure the quantum diode annealed at 700°C. For comparison, Fig. 3 shows efﬁciency, we deposited a nickel coating (instead of an the current dependences of the EL intensities at the Al coating), which transmitted one-sixth of the radia- maxima of the wavelength distributions (ELm) mea-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

EFFECT OF THE POSTIMPLANTATION-ANNEALING TEMPERATURE 37

1.0 1.2 1.4 1.6 400

12–11 Tann = 700°C 300 14–11 300 K

200 14– 9

12–9 Intensity, arb. units 80 K 100 12–7 14–7

Tann = 900°C 0 200 400 600 800 Current, mA

Fig. 3. Current dependences of the EL intensities at λ = 1.15 µm for (14Ð7, 14Ð9, 14Ð11) the KEF-500-based diodes and (12Ð7, 12Ð9, 12Ð11) the KÉF-0.5-based diodes. (14Ð7, 12Ð7) T = 700, (14Ð9, 12Ð9) 900, and (14Ð11, 12Ð11) 300 K ann 1100°C.

the current dependences of ELm, the internal quantum η efficiency int ceases to depend on the current at suffi- Intensity, arb. units ciently high currents. Figure 4 shows the current depen- 80 K dences of the internal quantum efficiency measured at 300 K on the KÉF-0.5-based diodes annealed in an Ar atmosphere. It is seen that, as the temperature of η postimplantation annealing increases, int increases monotonically and reaches its maximum (~0.4%) after annealing at 1100°C. This value far exceeds the room- Tann = 1100°C temperature quantum efficiencies of all other types of c-Si-based structures that radiate beyond the range of band-to-band transitions. Moreover, apart from structures where radiation is caused by defects or nanoinclu- 300 K sions, the intensity of band-to-band EL is not limited by the concentration of optically active centers. The experimental dependences of the effective minority-carrier lifetimes on the forward current con- 80 K structed for the same structures at 300 K are given in τ Fig. 5. The values of p were found to be independent of the current (at currents ≥100 mA) and to increase monotonically with the annealing temperature from τ ≈ µ ° τ ≈ µ ° p 1 s at Tann = 700 C to p 6 s at Tann = 1100 C. 1.0 1.2 1.4 1.6 A comparison of the experimental dependences shown λ, µm in Figs. 4 and 5 indicates that the values of quantum efficiency are approximately proportional to the effec- Fig. 2. EL spectra of KÉF-0.5-based diodes annealed at var- tive minority-carrier lifetimes. Insignificant variations η ious temperatures Tann. in ELm or int at high current densities were detected in the KÉF-500-based light-emitting diodes annealed sured at 300 K. For all samples, the current depen- under the same conditions. dences of ELm are virtually linear after a short initial The use of a chlorine-containing atmosphere instead nonlinear segment. Because of the linear character of of Ar for postimplantation annealing does not change

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 38 SOBOLEV et al.

6 0.4 1100°C 1100°C 5 0.3 4 s

1000°C µ , % , p

int 1000°C

τ 3 η 0.2 900°C 900°C 800°C 2 800°C 0.1 700°C 1 700°C

0 200 400 600 800 0 200 400 600 800 1000 Current, mA Current, mA

Fig. 4. Current dependences of the internal EL quantum Fig. 5. Current dependences of the minority-carrier lifetime efﬁciency at 300 K for the KÉF-0.5-based diodes annealed at 300 K for the KÉF-0.5-based diodes annealed in Ar at in Ar at various Tann. various Tann.

× the character of the current dependences of ELm and the foil. The total density of the rodlike defects is ~5 η 10 Ð2 int. However, the maximum values of internal EL 10 cm . Apart from the defects indicated above, this quantum efﬁciency are increased for the KÉF-500- sample contains closed prismatic dislocation loops 20Ð ° based diodes annealed at Tann = 900 C by 20% and at 100 nm in size with a density that is about two orders of ° Tann = 1000 C by 55% and for the KÉF-0.5-based magnitude smaller. Analysis of the available experi- diodes, by 35 and 75%, respectively. Approximately the mental data on the luminescence of c-Si subjected to same gains are detected for the minority-carrier life- radiation followed by annealing at 600Ð1100°C [6Ð8] times. This effect is caused by a decrease in the concen- indicates that the broad peaks of defect-induced EL in tration and, apparently, by a change in the type of non- question cannot be explained by the rodlike defects and radiative recombination centers because of the change closed prismatic dislocation loops alone. Therefore, in the annealing atmosphere. The value of this effect increases with the annealing temperature. Figure 6 shows spectra (measured at various temperatures) of the defect-induced EL in a KÉF-500- based sample annealed at 700°C. As is seen, the inten- 1.00 sity of the EL peak with a maximum at λ ~ 1.26 µm 80 K (measured at 80 K) decreases faster with increasing 115 K temperature than does the intensity of the broad EL 150 K band at λ ~ 1.2Ð1.6 µm. This can be due to the physical nature of the centers responsible for this peak and for this broad EL band being different. It is known [5] that annealing at 700°C of c-Si implanted with boron ions 0.10 leads to the formation of rodlike defects consisting of 207 K point-defect clusters and having various habit planes. Intensity, arb. units Indeed, the results of our electron-microscopic investigation showed that such defects were predominant in 300 K ° 245 K the KÉF-500-based structures annealed at Tann = 700 C (Fig. 7a). The projections of the defects are extended mainly along the 〈100〉 directions; however, there are 0.01 also defects oriented along the 〈110〉 directions. The 1.2 1.3 1.4 1.5 defect lengths vary signiﬁcantly and are 38–55 nm for λ, µm small defects and 220Ð270 nm for large ones. Conceiv- ably, the short defects are the defects that are inclined Fig. 6. EL spectra (measured at various temperatures) of a to the surface of a foil and cut during the preparation of KÉF-500-based diode annealed at 700°C.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 EFFECT OF THE POSTIMPLANTATION-ANNEALING TEMPERATURE 39

Thus, a high quantum efficiency of band-to-band [001] radiation that is sufficient for practical applications Si(100) (e.g., in silicon optrons) has been observed in light- emitting diodes containing structural defects of different nature with strongly different densities. Moreover, the EL quantum efficiency was maximum in a diode without extended structural defects. Analysis of the EL [010] and of the electrophysical and structural properties of the diodes indicates that, under the experimental conditions, structural defects affect the EL properties via the formation or gettering of nonradiative recombination centers rather than via preventing the removal of charge 250 nm (‡) carriers to the nonradiative recombination centers. For structures formed on low-doped substrates, the defects forming in c-Si as a result of implantation with boron ions and postimplantation annealing at a relatively low temperature (~700°C) can serve as a source of EL in the range 1.2Ð1.6 µm at various operating temperatures, including room temperature.

ACKNOWLEDGMENTS This work was supported in part by INTAS (grant no. 2001-0194), the Russian Foundation for Basic Research (project nos. 02-02-16374, 02-02-16692), and the Department of Physical Sciences of the Russian 0.5 µm (b) Academy of Sciences within the framework of the sci- entiﬁc program “New Materials and Structures.”

Fig. 7. Electron-microscopic images of a KÉF-500-based diode annealed in Ar at (a) 700°C (dark field, g = 〈220〉) and REFERENCES (b) 1000°C (bright field, g = 〈400〉). 1. Wai Lek Ng, M. A. Lourenco, R. M. Gwilliam, et al., Nature 410, 192 (2001). 2. A. A. Bergh and P. J. Dean, Light-Emitting Diodes (Clar- further studies are required to establish the physical endon, Oxford, 1976; Mir, Moscow, 1979). nature of optically active centers. A KÉF-500-based 3. B. Lax and S. F. Neustadter, J. Appl. Phys. 25 (9), 1148 ° sample annealed in Ar at Tann = 1000 C (at which light- (1954). emitting diodes were fabricated in [1]) contains Frank 4. R. A. Smith, Semiconductors, 2nd ed. (Cambridge Univ. loops and closed prismatic dislocation loops (Fig. 7b). Press, Cambridge, 1978; Mir, Moscow, 1982). The Frank loops have two characteristic sizes, 200Ð230 5. A. L. Aseev, L. I. Fedina, V. Hoehl, and H. Barch, Clus- tering of Interstitial Atoms in Silicon and Germanium and 380Ð515 nm. The total density of the Frank loops (Nauka, Novosibirsk, 1991). 8 Ð2 is about 4 × 10 cm . The closed prismatic dislocation 6. G. Davies, Phys. Rep. 176 (3Ð4), 83 (1989). loops are 50Ð190 nm in size, and their density is about 7. S. Coffa, S. Libertino, and C. Spinella, Appl. Phys. Lett. 2.5 × 108 cmÐ2. In the KÉF-500-based sample annealed 76 (3), 321 (2000). ° at Tann = 1100 C, no extended structural defects were 8. N. A. Sobolev, O. B. Gusev, E. I. Shek, et al., Appl. Phys. found, and the EL quantum efficiency in the range of Lett. 72 (25), 3326 (1998). band-to-band transitions at 300 K in this sample was higher than in the diodes containing extended defects. Translated by K. Shakhlevich

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Silicon LEDs Emitting in the Band-to-Band Transition Region: Effect of Temperature and Current Strength A. M. Emel’yanov, N. A. Sobolev, and E. I. Shek Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia e-mail: [email protected]

Abstract—The parameters of silicon light-emitting diodes (LEDs) prepared through boron implantation into n-Si, followed by annealing at 700Ð1200°C, were studied. The maximum room-temperature internal quantum efﬁciency of electroluminescence (EL) in the region of band-to-band transitions was estimated as 0.4% and reached at an annealing temperature of 1100°C. This value did not vary more than twofold within the operating temperature range 80Ð500 K. The EL growth and decay kinetics was studied at various currents. Following an initial current range of nonlinear dependence, the EL intensity scaled linearly with the current. It is shown that interpretation of this result will apparently require a revision of some present-day physical concepts concerning carrier recombination in silicon diodes. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION results thus obtained with measurements of the minority-carrier effective lifetimes. The luminescence associated with impurities and defects in Si single crystals (c-Si) has been attracting considerable interest over the past decade in connection 2. EXPERIMENTAL TECHNIQUES with the development of novel radiation sources for use We prepared pÐn junctions by using boron ion in optoelectronics. By contrast, the electrolumines- implantation at energy E = 40 keV to a dose D = 1 × cence (EL) of c-Si in the band-to-band transition region 1015 cmÐ2 into 0.37-mm-thick (100)-oriented KÉF-0.5 is known to a much lesser extent. Research in this area n-Si plates. To obtain Ohmic contacts, phosphorus ions appears to be important at least from the standpoint of (E = 75 keV, D = 1 × 1015 cmÐ2) were implanted into the providing a baseline for all other types of c-Si-based back side of the plates. Post-implantation anneals were light-emitting structures. Because of the indirect band- performed in an argon environment (at a temperature to-band transitions and very scarce relevant studies, c- Tt) for a duration of 20 min, followed by furnace-cool- Si was largely considered to hold little promise in the ing in Ar down to 600°C and subsequent removal to the development of high-efficiency light-emitting diodes air. T was varied from 700 to 1200°C in steps of 100°C. (LEDs) with a band-to-band emission spectrum. These t concepts were convincingly unproved only in recent All anneals were carried out with an 87-nm-thick ther- years, when it was shown [1, 2] that the quantum effi- mal SiO2 film present on the Si surface. The maximum EL quantum efficiency in the band-to-band region at ciency of band-to-band emission in c-Si at room tem- ° perature can be comparable to that of the light-emitting 300 K was reached at Tt = 1100 C. Therefore, all the diodes based on direct-band-gap semiconductors. Note graphs presented below refer to diodes fabricated at ° that the high quantum efficiency was obtained in [2] Tt = 1100 C. Diodes were formed using the standard using a relatively simple technique compatible with the mesa structure technology after deposition of Al elec- technique of integrated circuits; In [2], pÐn structures trodes on the front side of the plate and of Ni contacts were prepared through boron implantation into single- on the back side of the plate. The working areas of the crystal n-Si, with subsequent annealing at 1000°C. The pÐn junctions were 1.5 mm2. The EL was excited by structures reported here were also produced by ion applying a pulsed 32-Hz voltage to the diodes with implantation followed by annealing. The main goals of pulses 0.1Ð2.0 ms in duration. The EL spectra were our study were to (i) determine the post-implantation obtained with a monochromator, an InGaAs photode- annealing temperature that would be optimal for reach- tector, and a selective nanovoltmeter. When measuring ing the maximum EL efficiency, (ii) to investigate the the quantum efficiency, the radiation directed onto the variation of the EL parameters over an operating tem- entrance window of a Ge photodiode was collected by perature range broader than the one covered in [2], a lens system from the back side of the plate through a (iii) to measure the current dependences of the EL nickel coating, which transmitted 1/6 of the total radia- η intensity and quantum efficiency, (iv) to study the EL tion flux. The external quantum efficiency ext was kinetics at different currents, and (v) to compare the determined from measurements of the following quan-

SILICON LEDS EMITTING IN THE BAND-TO-BAND TRANSITION REGION 41

5 100 80 K 4

10 185 K 3

1 260 K 300 K Current, mA 2 Intensity, arb. units 375 K 0.1 1 435 K

0.01 0 0 0.4 0.8 1.2 1.6 1.0 1.1 1.2 1.3 Voltage, V λ, µm

Fig. 2. EL spectra of the diode under study measured at a cur- Fig. 1. Forward branch of the IÐV characteristic at 300 K. rent of 250 mA and various temperatures. Resolution 3 nm. tities: the photocurrent of the Ge photodiode, the cur- close to 300 K and higher. The long-wavelength shift of rentÐpower sensitivity, the solid angle within which the the EL spectrum with increasing temperature (Fig. 3) is radiation was collected, and the losses in the lens sys- associated primarily with the decreasing width of the c- tem, in the silicon (because the radiation was coupled Si band gap. Figure 4 displays the temperature depen- out the back side of the plate), and in the Ni coating. dence of the wavelength-integrated EL intensity The diode radiation was assumed to be isotropic within (ELIs). As is evident from Fig. 4, the light-emitting the hemisphere. It was also assumed that all of the radi- ° ation focused onto the entrance window of the FD-10 diodes can operate at least up to ~200 C. Because ELIs AG photodiode, which actually represented a minilens is directly proportional to the quantum efficiency at a built into the casing, was collected onto the photodetec- fixed current, the quantum efficiency is seen to vary by η tor sensitive area. The internal quantum efficiency int a factor of less than two in the temperature range stud- η η was calculated from the relation ext / int = 0.013 [3], which was derived theoretically for a plane junction LED and for a semiconductor refractive index equal to 1.24 τ 3.6. The effective minority carrier lifetime p was obtained, following the technique proposed in [4], from 1.22 measurements of the forward current pulse amplitude, as well as of the amplitude and duration of the part of the reverse current pulse corresponding to the phase of 1.20 the high inverse conductivity. The EL kinetics was

studied with the use of a germanium photodiode oper- m µ ating at room temperature. The response time of the , 1.18 m light-detecting device to a square light pulse in this λ regime of operation was 1 µs. 1.16

3. EXPERIMENTAL RESULTS AND DISCUSSION 1.14 The forward branch of the diode IÐV curve measured at 300 K is presented in Fig. 1. Figure 2 shows EL 1.12 spectra of the diode under study measured at 250 mA 100 200 300 400 500 and various temperatures in the band-to-band transition T, K region. It is usually assumed (see, e.g., [5]) that the EL in this spectral region is dominated by exciton-medi- λ Fig. 3. Temperature dependence of the wavelength m cor- ated radiative recombination at temperatures close to responding to the maximum of the EL intensity measured at 80 K and by free carrier recombination at temperatures a current of 250 mA.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

42 EMEL’YANOV et al.

0.10 0.10 0.5 0.5

ELIs 0.08 0.08 0.4 2 0.4

m 0.3 0.3 µ , %

, 0.06 0.06 int , arb. units , arb. units δλ 1 η δλ 0.2 0.2 ELIs 0.04 0.04 ELIs 0.1 0.1 0.02 0.02 0 0 100 200 300 400 500 0 200 400 600 800 1000 T, K Current, mA Fig. 4. Temperature dependences of the integrated EL intensity (ELIs) and of the peak half-width δλ measured at a cur- Fig. 5. Current dependences of (1) the integrated EL inten- rent of 250 mA. sity and (2) internal quantum efficiency measured at 300 K. ied. Figure 4 also displays the temperature dependence L of the EL peak half-width. Following a small initial η = βnpd x/()j/q range of nonlinear behavior, the dependences of inte- int ∫ grated EL intensity on current obtained in the diodes 0 under study at 80, 300, and 500 K are practically linear. L L L As a consequence, the quantum efficiency becomes = ∫βnpd x/ ∫γmpd x + ∫βnpd x (1) practically current-independent at high enough cur- η 0 0 0 rents. The current dependences of ELIs and int measured at 300 K are displayed in Fig. 5. The current L L dependences of the EL intensity at the maximum of the = ∫βnpd x/∫()p/τ dx, wavelength distribution do not differ in character from 0 0 the dependences of ELIs on current (Fig. 6). This suggests that the current can slightly heat the sample, where q is the elementary charge, j is the current den- which may produce EL spectral broadening. sity, L is the base thickness, x = 0 corresponds to the pÐ n junction, and τ is the minority-carrier lifetime. If τ η ≅ The ranges of the linear EL dependence on current does not depend on p, we have int const for at the maximum of the wavelength distribution of the β ≅ EL were also observed by us at other pÐn structure n const. (2) annealing temperatures. A linear variation of the band- Condition (2) is satisfied at low injection levels, where to-band EL intensity in c-Si and, accordingly, a current- p is considerably smaller than n. However, according to η independent ext (at high enough currents) have also our estimates, in the ranges of the linear ELIs current been observed in other studies [1, 6, 7]. However, no dependences obtained on our diodes, the conditions of explanation of this effect has been offered thus far. low injection level were, on the average, not met. A Variation of the density of the forward current through high injection level was also reported in the study of a a pÐn junction is accompanied usually by a variation in pÐiÐn structure described in [6]. Equation (2) is also the concentration p of the minority carriers (holes) in satisfied for β ~ 1/n. This conclusion is, however, in the diode base. Let us denote the concentration of elec- conflict with the universally accepted concepts [6, 8, 9]. trons in the conduction band of the diode n base by n η As follows from Eq. (1), the condition int = const and the concentration of the recombination levels filled can also be met if with electrons by m. Then, the number of band-to-band radiative recombination events per unit time per unit m = αn, (3) β volume will be np and that of nonradiative recombina- α tion events will be γmp (where β and γ are coefficients where is a coefficient of proportionality. In this case, characterizing the recombination probabilities). Recall- we obtain ing the definition of the internal quantum efficiency (in η = β/()αγ+ β (4) equilibrium conditions) of a nonsymmetrical pÐn junc- int tion in which the recombination occurs in the diode and, therefore, τ varies with n (in inverse proportion). base, we can write This dependence is at odds with the nonradiative-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 SILICON LEDS EMITTING IN THE BAND-TO-BAND TRANSITION REGION 43

400 1.0 1.0 80 K 300 0.8 0.8 300 K 0.6 0.6 200 EL 0.4 Current 0.4 435 K Voltage Intensity, arb. units Intensity, arb. units 100 0.2 0.2

0 0 Normalized voltage and current, arb. units 0 10 20 30 40 50 60 70 t, µs 0 100 200 300 400 500 Current, mA Fig. 7. EL kinetics (EL) and the corresponding evolution of Fig. 6. Current dependences of the EL intensity at the wave- the diode voltage and current normalized against their max- length corresponding to its maximum measured at various imum values measured at 300 K and a current pulse ampli- temperatures. tude of 300 mA. recombination theory of ShockleyÐRead, according to For t = τ, we have P ≅ 0.63( jτ/q) = 0.63P (where τ max which should be independent of n and p at a high Pmax is the maximum value of P). If condition (2) is injection level [10]. Note that the experimentally met, the quantity P is directly proportional to the EL τ observed p being practically independent of current intensity; therefore, in our case, the EL intensity should cannot be considered unambiguous evidence that the reach a value equal to 0.63 of its maximum value in dependence of τ on p is absent, at least for the reason time t ≅ τ. The kinetics of the EL rise and decay mea- τ that the relation proposed in [4] for determining p was sured with our diode at a current of 300 mA and tem- derived for the case of τ being independent of p (see, for perature of 300 K is presented graphically in Fig. 7. At instance, [10]). The value of β was calculated theoreti- 300 K, the time needed for the EL intensity to reach αγ cally [6, 8, 9], and in our case can be obtained from 0.63 of the maximum level, τ , was about 9 µs for all η 0.63 Eq. (4) using int measurements. currents studied in the range 80Ð500 mA. The EL decay τ If all carriers injected into the base become bound to time constant and p were also practically current-inde- form excitons, we have pendent within the above range and constituted ~6 µs. L L With due account of the inertia in the operation of the η = ()w/ξ dx/ ()w/τ dx, (5) light-measuring system, as well as of the delay in the int ∫ ∫ current amplitude value becoming steady (Fig. 7) and 0 0 τ of the error in the p measurement, the difference found where w is the exciton density and ξ is the exciton radi- between the measured values of τ and τ cannot be ξ η p 0.63 ative lifetime. If = const, the condition int = const is considered to contradict the model used here. Said oth- satisfied for τ = const. erwise, the experimental results obtained here are not at In the case where τ does not depend on p and con- variance with the assumption of τ being independent of dition (2) is upheld, one can derive an expression p and of condition (2) being valid. The delay in the describing the rise in the band-to-band EL intensity onset of the current with respect to the voltage (Fig. 7) with the time t elapsed since the application of a square in the diode under study should be probably assigned to current pulse of density j to the structure. As before, we modulation of the base resistance [10]. Note that, other τ consider a nonsymmetric pÐn junction and recombina- conditions being equal, 0.63 decreased as a result of the L τ tion in the diode base. With the notation ∫ pxd = P, factors causing the decrease in p, for instance, a 0 decrease in T or in the diode operating temperature. the rate of variation of the quantity P with time can be t Other publications [1, 2, 6] dealing with investigation written as of the parameters of high-efficiency silicon light-emit- dP/dt= j/qPÐ /τ. (6) ting diodes did not present the results of direct measure- τ The solution to Eq. (6) is ments of p [2, 6] or of the EL kinetics [1]. This makes comparison of our results with the results obtained in Pt()= ()jτ/q []1 Ð exp()Ðt/τ . (7) the above studies difficult.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 44 EMEL’YANOV et al. η Assuming that int is independent of current due to results of the comparison are not inconsistent with the condition (3) being met, the equation for the variation assumption of the lifetime τ and of the quantity βn in quantity P with time needed to describe the EL inten- being independent of minority-carrier concentration. sity rise kinetics can be cast in the form L ACKNOWLEDGMENTS dP/dt= j/q Ð ()αγ+ β ∫npd x. (8) This study was supported by INTAS (grant no. 0 2001-0194), the Russian Foundation for Basic Research (project no. 02-02-16374), and the Russian We readily see that this equation does not have a simple Academy of Sciences (Physical Sciences Division) solution and requires that additional conditions be for- program “New Materials and Structures.” mulated, because, unlike Eq. (6), it contains two (P and L npd x ) rather than one (P) unknown which vary with ∫0 REFERENCES time. 1. M. A. Green, J. Zhao, A. Wang, et al., Nature 412, 805 (2001). 4. CONCLUSIONS 2. Wai Lek Ng, M. A. Lourenco, R. M. Gwilliam, et al., Nature 410, 192 (2001). To sum up, by using boron implantation into n-Si 3. A. A. Bergh and P. J. Dean, Light-Emitting Diodes (Clar- and subsequent annealing, we have prepared silicon endon, Oxford, 1976; Mir, Moscow, 1979). light-emitting diodes with a high internal quantum EL 4. B. Lax and S. F. Neustadter, J. Appl. Phys. 25 (9), 1148 efficiency (according to our estimates, up to ~0.4%) in (1954). the band-to-band transition region. This efficiency var- 5. R. A. Smith, Semiconductors, 2nd ed. (Cambridge Univ. ied less than twofold within the operating temperature Press, Cambridge, 1978; Mir, Moscow, 1982). interval from 80 to 500 K. The presence of a range of 6. Th. Dittrich, V. Yu. Timoshenko, J. Rappich, and linear dependence of the EL intensity on current has L. Tsybeskov, J. Appl. Phys. 90 (5), 2310 (2001). been demonstrated to be a fairly typical property of high-efficiency silicon band-to-band LEDs prepared by 7. W. Michaelis and M. H. Pilkuhn, Phys. Status Solidi 36, 311 (1969). different techniques and operating at various temperatures. It was first shown that interpretation of this effect 8. W. van Roosbroeck and W. Shockley, Phys. Rev. 94 (6), 1558 (1954). would apparently require revision of some heretofore accepted concepts, such as the minority carrier lifetime 9. R. D. Altukhov and E. G. Kuzminov, Solid State Com- being constant or the radiative-recombination probabil- mun. 111, 379 (1999). ity of the electrons and holes remaining unchanged 10. Yu. R. Nosov, Switching in Semiconductor Diodes under variation of the injected carrier concentration at (Nauka, Moscow, 1968; Plenum, New York, 1969). τ high injection levels. The kinetics of the EL and of p were measured and compared for the first time. The Translated by G. Skrebtsov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 45Ð48. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 49Ð52. Original Russian Text Copyright © 2004 by Blonskyy, Vakhnin, Kadan, Kadashchuk.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) New Mechanisms of Localization of Charge Carriers in Nanosilicon I. V. Blonskyy, A. Yu. Vakhnin, V. N. Kadan, and A. K. Kadashchuk Institute of Physics, National Academy of Sciences of Ukraine, pr. Nauki 46, Kiev, 03028 Ukraine e-mail: [email protected]

Abstract—This paper reports on the results of investigations into the spectral dependences of thermally stimulated luminescence and the temperature dependences of tunneling luminescence in highly oxidized porous silicon samples. Two new mechanisms of localization of charge carriers are considered in terms of the speciﬁc features revealed in the spectral dependences of the thermally stimulated luminescence and nonmonotonic temperature dependences of the Becquerel index of tunneling luminescence decay. The proposed mechanisms of charge carrier localization are associated with structure heterogeneities inherent in these objects, namely, ≤ superﬁcial SiOx oxide shells (0 < x 2) enclosing silicon particles and an undulating structure of silicon wires. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION localized states in low-temperature PL spectra of two- dimensional structures resemble those observed for The localization of charge carriers and excitons in semiconductor solid solutions. However, there are semiconductor media of different dimension is one of some differences associated with the two-dimensional the most important electronic phenomena. As is known, nature of the density of states (see, for example, [3]). In there are many mechanisms responsible for the local- quasi-one-dimensional and quasi-zero-dimensional ization of electronic excitations. In this paper, we will structures, the processes of localization of electronic not concern ourselves with all these mechanisms but excitations and their spectral manifestations are less will dwell briefly on only two of them. The localization well understood. This can be judged from the ongoing mechanisms we are interested in are associated with the discussion of the nature of the main luminescence band dimensionality of the medium and clearly manifest for porous silicon. As is known, highly oxidized porous themselves in low-temperature photoluminescence silicon samples consist of a complex mixture of quasi- (PL). The first mechanism, which is characteristic of zero-dimensional and quasi-one-dimensional silicon three-dimensional media, governs the localization of particles enclosed in superficial SiOx oxide shells (0 < electronic excitations in semiconductor solid solutions. x ≤ 2) involving different trapping states. These states These objects exhibit partial composition disordering, are primarily responsible for the luminescence proper- and, consequently, the crystal potential contains a fluc- ties of porous silicon materials, even though their role tuation component of the white-noise type. In the case is not completely understood. In our previous works [4, where the energy, geometric, and kinetic criteria are 5], we proposed a model of filling of trapping states met, the potential wells encourage the localization of upon photoexcitation of the silicon core through an excitons and charge carriers, which is accompanied by Auger electron process occurring under conditions of inhomogeneous broadening of the localized states. spatial confinement of carriers, i.e., in an activation Algorithms for determining the parameters of localized manner. In nanoparticles, the Auger electron process states have been developed and their validity has been dominates, because the cross section W of this process confirmed for II–VI semiconductor solid solutions on varies with an increase in the distance R between inter- the basis of both the theoretical models proposed for acting particles as W ~ RÐ6. For example, at R ≈ 10 nm, these systems (see, for example, [1]) and the low-tem- ≈ 15 Ð2 perature PL data obtained by selective excitation tech- we obtain W 10 cm , which almost coincides with niques (see, for example, [2]). the cross section of the unit cell. According to the proposed model of a “two-stroke charge piston,” the charge The mechanism of localization of electronic excita- piston acts in turn on the electron and hole components tions in two-dimensional structures (for example, due to the Auger electron process and pushes them into superlattices) is similar in many respects to the first SiOx shells, followed by localization of the charge car- mechanism. It is known that, in two-dimensional riers [4, 6]. This model offers a satisfactory explanation objects, the fluctuation component of the crystal poten- for a number of features of the main luminescence tial is determined by the variation in the quantum-well band in the spectra of porous silicon, namely, the non- width. In general, the features of the manifestation of monotonic temperature dependence of the integrated

46 BLONSKYY et al.

40 trapping states. Investigation into the spectral composi- (a) tion of thermally stimulated luminescence is of particular interest, especially with due regard for the spatial 30 inhomogeneity of silicon nanocrystallites and for the purpose of revealing a correlation between the nanoc- 20 rystallite structure (silicon core, peripheral SiOx oxide shells, x ≤ 2) and the shape of the TSL spectrum. It should be noted that, for highly oxidized porous silicon, 10 λ the nature of the main reddish orange PL band ( max = 680 nm) remains rather controversial, whereas the 0 weaker blue band (λ = 440 nm) is almost universally (b) max 20 assigned to defect states of SiOx shells. Therefore, with knowledge of the correlation between the spectral com- 15 position of the photoluminescence (in particular, the blue emission band) and the shape of the TSL spectrum, it is possible to judge occupation of traps of an

, arb. units 10 SiOx shell upon photoexcitation of the silicon core and TSL I 5 to determine their activation energies EA. In this work, we will not dwell on the experimental 0 techniques used in our measurements, because they 12 1.4 (c) were thoroughly described in our earlier works [3, 6]. 1.0 Note only that the spectral dependences of the thermally stimulated luminescence were measured either 8 0.6 during heating at a rate of 0.15 K/s or upon fractional , arb. units thermoluminescence. The results of these measure- PL I 0.2 ments are presented in Fig. 1. Without going into 4 details (also described in [3, 6]), we draw the main con- 400 500 600 700 clusion that there is a one-to-one correspondence λ, nm λ between the main PL band ( max = 680 nm) and the broad TSL component (at ≈90 K), on the one hand, and 0 50100 150 200 250 λ Τ, Κ the blue PL band ( max = 440 nm) and the narrow TSL doublet (at 25 K), on the other. This suggests that the Fig. 1. Spectral dependences of the thermally stimulated luminescence in highly oxidized porous silicon samples: trapping states of the oxide shells are filled upon photo- (a) the total PL spectrum, (b) PL in the wavelength range excitation of the silicon core. The above inference is λ > 640 nm, and (c) PL in the wavelength range λ < 580 nm. supported by the results obtained by Kux et al. [7], who The inset shows a typical PL spectrum of porous silicon. studied the temperature dependence of the decay kinetics of the blue PL band. It was revealed in [7] that, upon cooling from room temperature to liquid-helium tem- intensity, nonlinearity of the luminous characteristics, perature, the decay kinetics (apart from the main nano- spectral dependence of the “luminescence decay” second component) exhibits a millisecond component effect, etc. However, in our opinion, the proposed beginning from approximately 30 K. These authors model calls for further experimental corroboration. In brought forward a number of arguments in support of this respect, one of the main objectives of the present the assignment of the millisecond component to shal- work was to verify experimentally the validity of the low-lying (≈25Ð30 K) trapping states of the peripheral model of a two-stroke charge piston. Moreover, we oxide layers. All these findings count in favor of the revealed the specific features of localized states in one- model of a two-stroke charge piston [4, 5]. dimensionally irregular media. For this purpose, we investigated the spectral dependences of thermally Thermally stimulated luminescence is characterized stimulated luminescence (TSL) and the temperature by a feature that is also specific to the reddish orange dependences of tunneling luminescence in highly oxi- PL band. The case in point is the extremely large width dized porous silicon samples prepared using a standard of the high-temperature TSL component, which indi- procedure. cates considerable dispersion of the activation energy EA. The temperature dependence of the activation energy EA can easily be determined from the experi- 2. SPECTRAL DEPENDENCES OF THERMALLY mental data presented in Fig. 1 and the algorithms pro- STIMULATED LUMINESCENCE posed in [3, 5]. The dependence thus obtained is depicted in Fig. 2. It should be noted that the limiting ≈ Thermally stimulated luminescence is a universally value EA 0.3 eV is approximately equal to the half- accepted tool for studying the activation spectrum of width of the reddish orange PL band. In order to eluci-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

NEW MECHANISMS OF LOCALIZATION OF CHARGE CARRIERS 47 date the nature of the broad spectrum of the activation luminescence is characterized by a very low intensity Ðβ β ≈ energy of trapping states related to the silicon core, we and decay of the Becquerel type (Ilum ~ t , where analyzed several models. In this paper, we will briefly 1). In our experiments, the kinetics of tunneling lumi- consider the most realistic model associated with one nescence was measured after completion of the photo- more type of structural heterogeneity of porous silicon, excitation of the samples at delay times ranging from an undulating structure of individual silicon wires. The 1 to 1000 s and a signal buildup time of ≈1 s. Moreover, results of numerous structural investigations of porous we examined how the temperature affects the kinetics silicon indicate that variations in the thickness of an of tunneling luminescence in the range from 4.2 to individual silicon wire can be significant and irregular; 300 K. The results obtained are thoroughly described in moreover, these variations are observed for wire seg- [4, 5]. In the present work, we will discuss new aspects ments of different lengths. From analyzing the standard of the problem under investigation. Figure 3 shows the expression relating the energy of electronic excitations temperature dependence of the Becquerel index β(T) to the crystallite sizes along the quantum-confinement calculated from the data reported in [4, 5]. It is worth axis, we can infer that the above structural features of noting that the dependence β(T) exhibits nonmonotonic silicon wires should favor the formation of a one- behavior. We attempted to interpret the nonmonotonic dimensional fluctuation component of the crystal dependence β(T) in the framework of different theoret- potential whose wells at certain parameters can be ical approaches that account for tunneling charge trans- treated as topological traps (see insets to Fig. 2). In this fer in an ensemble of localized states. In our opinion, case, the dispersion of the activation energy E = 0.3 eV A the approaches developed by the group of researchers could reflect a wide scatter in the thicknesses of differ- under the guidance of Goldanskii (see [8]) and ent segments of the silicon wire. Although this scatter Arkhipov et al. [9] provide the most correct qualitative in the thicknesses is actually observed within both an explanation of the dependence β(T). Following these individual wire and an ensemble of wires, the proposed approaches, all centers of charge carrier localization are model should be considered only a hypothesis. With the aim of justifying this model, we investigated the tem- divided into two groups. The first group involves cen- perature dependences of the tunneling luminescence ters separated by distances that exclude the possibility and analyzed the obtained results in the framework of of charge transfer occurring between them. These are approaches developed by different authors. typical isolated traps playing the role of sinks for charge carriers. The second group consists of centers spaced at distances that allow charge transfer between 3. TEMPERATURE DEPENDENCES them. Goldanskii and coworkers referred to these OF TUNNELING LUMINESCENCE ensembles as diffusion clusters. According to [8, 9], electron transfer can occur through two mechanisms The recombination of charge carriers due to tunnel- depending on the nature and degree of disordering of ing transitions is accompanied by the emission of light, the medium: (i) the mechanism of hopping migration which is referred to as tunneling luminescence. This (over isolated centers) [8] and (ii) the mechanism of

V 0.3 V0 1.0

0.2 D0 0.9 , eV β A E 0.1

0.8

0 50 100 150 T, K 0.7 0 50 150 250 Fig. 2. Temperature dependence of the average activation T, K 〈 〉 energy EA for trapping states. Insets illustrate the origin of topological traps in silicon wires due to variations in their Fig. 3. Temperature dependence of the Becquerel index β of diameter D0. tunneling luminescence decay.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

48 BLONSKYY et al. multiple retrapping [9]. The latter mechanism, in topological traps upon thermally stimulated lumines- essence, is as follows. A charge carrier undergoes trans- cence and tunneling luminescence. fer through thermally activated hopping from the trapping state to the nearest band state, executes diffusive motion until another trap located at a point of the space ACKNOWLEDGMENTS is attained, is retrapped at this point, again undergoes This work was supported by the Intergovernmental thermally activated transfer to a band state, is retrapped Russian–Ukrainian program “Nanophysics and Nano- at a new point of the space, etc. This process is called electronics” (grant “Electrical and Optical Properties of dispersive transport or non-Gaussian diffusion. Making Nanostructures Based on Silicon and Germanium”) and allowance for the possible retrapping of charge carriers, the program of the National Academy of Sciences of Berlin et al. [8] derived a relationship for the Becquerel Ukraine “Physical and Astrophysical Basic Research in index. On this basis, we can explain the nonmonotonic the Structure and Properties of Matter on the Macro- behavior of β(T). By generalizing the above model to scopic and Microscopic Levels.” porous silicon with an irregular structure of silicon wires (see insets to Fig. 2), we assumed that very short thick segments of silicon wires serve as isolated trap- REFERENCES ping centers (topological traps), whereas extended seg- 1. E. Cohen and M. D. Sturqe, Phys. Rev. B 15 (2), 1039 ments of silicon wires with a constant thickness play (1977). the role of band states. The multiple retrapping of 2. S. Permodorov, A. Resznitsky, and S. Verbin, Phys. Sta- charge carriers between these regions can be responsi- tus Solidi B 113 (2), 589 (1982). β ble for the nonmonotonic dependence (T) (Fig. 3). 3. I. V. Blonskiœ, V. N. Karataev, D. D. Kolendritskiœ, et al., The proposed hypothesis is in reasonable qualitative Fiz. Tverd. Tela (St. Petersburg) 34 (10), 3256 (1992) agreement with the assumption regarding the influence [Sov. Phys. Solid State 34, 1742 (1992)]. of topological traps on the shape of the TSL spectrum. 4. I. V. Blonskiœ, M. S. Brodin, A. Yu. Vakhnin, et al., Fiz. However, this hypothesis calls for more rigorous theo- Nizk. Temp. 28 (8/9), 978 (2002) [Low Temp. Phys. 28, retical justification. 706 (2002)]. 5. I. V. Blonskiœ, M. S. Brodin, A. Yu. Vakhnin, et al., Mik- 4. CONCLUSIONS rosist. Tekh., No. 2 (2003) (in press). 6. I. V. Blonskyy, M. S. Brodyn, A. Yu. Vakhnin, et al., Thus, the results obtained in this work lent support Phys. Lett. A 279, 391 (2001). to the validity of the proposed model of a two-stroke 7. A. Kux, D. Kovalev, and F. Koch, Appl. Phys. Lett. 66 charge piston that acts in turn on the electron and hole (1), 49 (1995). components due to an Auger electron process occurring under conditions of spatial confinement of charge car- 8. Yu. A. Berlin, N. I. Chekunaev, and V. I. Goldanskii, riers in silicon nanoparticles. This model offers a satis- J. Chem. Phys. 92 (12), 7540 (1990). factory explanation for both the activation nature of the 9. V. I. Arkhipov, V. R. Nikitenko, and A. I. Rudenko, Fiz. localization of charge carriers in traps of oxide shells Tekh. Poluprovodn. (Leningrad) 21 (4), 1125 (1987) and the charge accumulation in these shells. [Sov. Phys. Semicond. 21, 685 (1987)]. Moreover, we revealed the specific features of the one-dimensional confinement of charge carriers in Translated by O. Borovik-Romanova

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 49Ð55. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 53Ð59. Original Russian Text Copyright © 2004 by Egorov, Cirlin, Tonkikh, Talalaev, Makarov, Ledentsov, Ustinov, Zakharov, Werner.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Si/Ge Nanostructures for Optoelectronics Applications V. A. Egorov1, 2, 4, G. É. Cirlin1, 2, 4, A. A. Tonkikh1, 2, 4, V. G. Talalaev3, 4, A. G. Makarov2, N. N. Ledentsov2, V. M. Ustinov2, N. D. Zakharov4, and P. Werner4 1 Institute of Analytical Instrumentation, Russian Academy of Sciences, Rizhskiœ pr. 26, St. Petersburg, 190103 Russia e-mail: [email protected]; [email protected] 2 Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia 3 Fock Institute of Physics, St. Petersburg State University, ul. Pervogo Maya 100, Petrodvorets, St. Petersburg, 198504 Russia 4 Max-Planck-Institut für Mikrostrukturphysik, Halle(Saale), D-06120 Germany

Abstract—The optical and structural properties of multilayer Si/Ge structures with precritical, as well as close- to-critical, germanium inclusions in a silicon matrix, for which the transition from the two-dimensional to island growth occurs, were studied. The possibility of obtaining intense photoluminescence at room temperature in both cases under optimally chosen growth parameters is demonstrated. The proposed approaches to producing an active region appear promising for applications in silicon-based optoelectronics. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION rier collection to the recombination region and, thus, to reach a high luminescence intensity at room tempera- We are presently witnessing a considerable world- ture. The above considerations stimulate the search for wide interest in the search for possible ways to develop new ways to solve the problem of increasing the effi- silicon-based light-emitting semiconductor devices. ciency of radiative recombination in silicon-based Efficient radiative recombination in silicon is compli- semiconductor structures. cated by its indirect-band-gap structure; however, if a means of increasing the efficiency is found, this would The first part of this report proposes a method of immediately make it possible to integrate optoelectron- carrier localization in the active region consisting of ics and modern microelectronics devices on the same nanometer-sized Ge islands with lateral dimensions substrate, with silicon forming the basis. The presently less than the hole Bohr radius obtained through molec- known approaches to solving this problem are the use ular-beam epitaxy (MBE) deposition of submonolayer of porous silicon [1], quantum wells in the Si/Ge sys- coatings of germanium on silicon. Such inclusions tem, and Si/Ge and Si/Ge/C quantum dots [2], as well should give rise to a partial change in the wave-vector as of InAs/Si [3] and other direct-band-gap IIIÐV mate- selection rules and to the possible formation of a local- rials, and the doping of silicon by rare-earth elements ized exciton (which forms in the interaction of a free [4]. These approaches have met with partial success electron with a hole bound to a germanium island) that and also have certain shortcomings. For instance, pre- is stable up to room temperatures, thus increasing the paring high-quality heteroepitaxial layers on a Si surface needed to obtain quantum wells and quantum dots radiative recombination efficiency. This situation can is complicated by the lattice misfit, which accounts for be realized in the cases where the Coulomb attraction a large number of defects in the growing layer of the energy for the electron is stronger than the repulsive material, and by the generation of strains in a IIIÐV potential barrier created by the germanium nanoisland semiconductor layer because of a considerable differ- in the conduction band. To increase the radiative ence between the linear-expansion coefficients of Si recombination efficiency further, we propose perform- and of the IIIÐV material. Doping Si by rare earth ele- ing multiple vertical stacking of layers containing ger- ments, for instance, by erbium, gives rise to impurity manium submonolayer inclusions separated by a sili- luminescence, whereas successful device application con spacer. The proposed technique for obtaining sub- (in particular, for injection lasers) requires efficient monolayer inclusions of germanium in a silicon matrix band-to-band luminescence. The possibility of prepar- makes it possible to attain a good localization of holes ing a fast germanium detector integrated on a silicon and, accordingly, of excitons; the islands should be chip was demonstrated in [5]. However, when using coherent because of their small size, and the accumu- Ge/Si quantum wells (both materials have an indirect lated elastic strains in the structure would be small band-gap structure) as active elements for light-emit- because of the small amounts of germanium used as the ting devices, it is not possible to achieve efficient car- active regions, which gives grounds to expect a good

50 EGOROV et al.

Si-TO 1.099 eV

1.099 eV Si-TO 1.068 eV Ge-TO b

1.036 eV Ge-TO Ge-NP 1.125 eV Si-TO + O Ge-NP 1.138 eV PL intensity, arb. units PL intensity, arb. units c Si-TA

a ×3 d 0.95 1.00 1.05 1.10 1.15 1.20 1.25 0.98 1.02 1.06 1.10 1.14 1.18 Photon energy, eV Photon energy, eV

Fig. 1. PL spectra obtained at 15 K on samples with (a) 0.5 and (b) 1.0 ML of Ge in each unit layer of the structure and on samples prepared (c) in the growth-interrupting mode after deposition of each Ge layer and (d) without growth interruption. crystallographic quality and low density of defects rep- 0.02–3 Å/s, respectively, in this growth process. The resenting nonradiative recombination centers. pressure in the growth chamber in these experiments × Ð10 In the second part of this work, the fabrication of was less than 5 10 Torr. The deposition of the active defect-free multilayer Si/Ge structures with quantum region was monitored in situ by using high-energy elec- dots that radiate in the vicinity of 1.55 µm at room tem- tron diffraction in the reﬂection geometry. The photolu- perature is reported. The integrated intensity of the pho- minescence (PL) was excited by an Ar+ laser (λ = toluminescence band originating from the quantum-dot 488 nm). To measure the PL dependence on pump den- radiation features a superlinear dependence on the opti- sity, the laser beam was focused on a spot 103 µm2 in cal pumping density. The results of studies of the opti- area on the sample surface. The PL temperature depen- cal and structural properties of such systems as func- dence was measured in a helium cryostat. The PL signal tions of the growth parameters are presented. was collected by a monochromator interfaced to a Ge photodetector cooled by liquid nitrogen (Edinburgh Instruments, Inc). In constructing the PL dependences 2. EXPERIMENT on pump power, the spectra were normalized against the photodetector sensitivity. The structural studies The experimental samples were MBE grown on were conducted using transmission electron micros- semi-insulating Si(100) substrates in a Riber SIVA45 copy (TEM) on a JEM 4010 (accelerating voltage setup. The substrates were subjected to a pregrowth 400 kV) and CM 20 (200 kV). chemical treatment [6] to ensure removal of the oxide ° layer under heating to Ts = 840 C. The deviation from uniformity of the temperature distribution ﬁeld pro- 3. RESULTS AND DISCUSSION duced by the substrate heater with a rotated sample did not exceed 5%. The samples actually represented a 3.1. Si/Ge Structures with Submonolayer Inclusions ° buffer silicon layer 100 nm thick (grown at Ts = 600 C), Our earlier studies of the optical properties of Si/Ge Ge/Si (20 pairs) superlattices, and a 20-nm-thick sili- structures with submonolayer germanium inclusions con cap layer. The thickness of a Ge layer was 0.7–9 Å, [7] revealed new lines in the PL spectra of these sam- and that of a silicon spacer, 40–50 Å. The growth tem- ples; these lines were not observed in the spectrum of perature of the active region was 600Ð750°C. In several the silicon substrate and were assigned to radiation samples, the silicon spacer was doped by an n-type from the Si/Ge superlattice. Interestingly, if an integer impurity (Sb). The growth rates for Si and Ge, main- number of Ge monolayers was deposited, the integrated tained constant by means of mass spectrometers tuned intensity of the corresponding PL peak was ~20 times to atomic masses 28 (Si) and 74 (Ge), were 0.5 and weaker than in the case of deposition of 0.5 ML

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Si/Ge NANOSTRUCTURES FOR OPTOELECTRONICS APPLICATIONS 51

(Figs. 1a, 1b). Structural studies showed that a germanium layer obtained by depositing an integer number of 5 mW/cm2 monolayers is practically monatomic, whereas in a sub- Ar monolayer film germanium merges to form nanois- 15 K lands up to a few monolayers thick [8]. The differences in the structural and optical properties can be accounted for in the following way. The film of a monolayer coverage is singular, while in the case of the surface being InAs QD in incompletely covered local nonuniformities form on it. InGaAs QW When the substrate material is deposited on top, the generated elastic stresses can favor the creation of three-dimensional islands under certain conditions. The island size is governed by the balance between the elastic and surface energies. If two-dimensional nuclei Si/Ge doped SML are smaller than the critical size, it is energetically pref- PL intensity, arb. units × erable for the islands to have a three-dimensional struc- 100 ture, while larger islands retain their planar form. In our case, deposition of 0.5 ML Ge produces first relatively small germanium islands of monatomic height on the silicon surface, because this amount of material is insufficient to cover the whole surface. After that, these plane islands are overgrown by a silicon spacer, which changes the balance between the surface and elastic 1.00 1.05 1.10 1.15 1.20 1.25 energies. If these islands are less than the critical size, E, eV they transform from planar to three-dimensional; other- Fig. 2. Comparison of PL spectra of InAs quantum dots in wise, they retain their shape. an InGaAs quantum well and of a Sb-doped Si/Ge multi- To substantiate this mechanism, we prepared sam- layer quantum-dot structure. ples by interrupting the growth immediately after the Ge layer deposition. The growth-interrupting mode stimulates germanium adatom migration over the sur- [9]. It should be pointed out that our doped Si/Ge sam- face, with the result that plane nanoislands thus ple with submonolayer inclusions produces a PL inten- obtained are larger in size than those obtained without sity only two orders of magnitude lower than that of the the interruption. Figures 1c and 1d display PL spectra sample with direct-gap InAs quantum dots in a GaAs for samples grown without interruption and with a matrix. Furthermore, we have recently demonstrated 120-s interruption. In the spectrum obtained in the sec- that the integrated PL intensity exhibits a superlinear ond case, the PL peak corresponding to radiation from dependence on excitation density [10] in Si/Ge struc- the Si/Ge superlattice practically cannot be seen. TEM tures with submonolayer Ge inclusions, which makes observations likewise do not reveal any three-dimen- the above method a promising approach for developing sional nanoislands in the sample prepared in the silicon-based light-emitting devices. growth-interrupting mode. These results show that, in this case, the two-dimensional islands were above the critical size, so that overgrowth by the silicon spacer 3.2. Si/Ge Quantum-Dot Structures did not stimulate the formation of three-dimensional inclusions and the Ge islands retained their plane We studied structures made up of 20 Ge layers 0.7- shape. to 0.9-nm thick separated by a 5-nm-thick silicon Because the holes in the Ge islands become effi- spacer. After deposition of the Ge layer, the surface was ciently localized in the Si/Ge structures under study, maintained in a Sb flux for 20–30 s (delta doping); as a while electron localization in the islands is partially result, the adjoining 2 nm of the spacer were doped by suppressed by the repulsive potential of the barrier, we an n-type impurity, while the remaining 3 nm of the proposed additional doping of the matrix by an n-type spacer were left undoped. Figure 3 presents typical impurity as a means of increasing the PL intensity. With TEM images of the cross section (Fig. 3a) and surface an optimally chosen doping level, the PL efficiency plane (Fig. 3b) of the Si/Ge quantum-dot structures increases by up to 50 times compared to the undoped under study. Despite the small spacer thickness, the structure. Figure 2 shows PL spectra measured at 15 K structures do not exhibit any structural defects. We on a doped Si/Ge sample and an InAs sample with clearly see Ge islands with lateral dimensions of quantum dots in an In0.12Ga0.88As quantum well (thus ~80 nm whose height varies from 3 to 5 nm. The high- permitting intense generation at a wavelength of 1.3 µm est islands are located in the central part of the struc- at room temperature). The internal quantum efficiency ture. The average surface density of the islands as esti- of the latter sample was estimated to be close to 100% mated from Fig. 3b is ~1 × 1010 cmÐ2 in each layer. The

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

52 EGOROV et al.

Si Ge Si Ge Si Ge Si Ge Si Ge z Si Ge Si Ge (‡) x 10 nm (b) 500 nm

Fig. 3. High resolution TEM images (a) of a cross section and (b) of the surface plane of an optimized Ge/Si sample with quantum dots.

(a) (b) 8 K 106 J ~ Pm 300 K m = 1.15 105 , arb. units J 104 QD SiTO 103

102 m = 1.65 PL intensity, arb. units ×1 101 Integrated PL intensity ×10 100 0.8 0.9 1.0 1.1 1.2 101 102 103 104 Photon energy, eV Excitation power density P, W/cm2

Fig. 4. (a) PL spectra of an optimized Ge/Si quantum-dot sample for an excitation density of 1 W/cm2 and (b) pump density dependence obtained at room temperature. islands are highly ordered in both vertical and horizon- ties, from 3 to 6000 W/cm2. At higher excitation levels, tal directions. the PL intensity continues to follow a superlinear relation with m = 1.15. As far as we know, this type of rela- Figure 4a displays PL spectra obtained at room and tion has never been observed in second-order transi- liquid-helium temperatures for a Ge/Si quantum-dot tions in the Si/Ge system. For instance, the exponent m sample prepared under the optimally chosen growth for the Si/Ge quantum-dot system studied in [11] was conditions. The PL radiation emitted from the Ge quan- estimated as 0.78 for the quantum-dot PL (second- tum dots (the corresponding peak is denoted by QD) order transition) and as 0.96 for the radiation from the remains fairly intense even at room temperature, and its wetting layer (quasi-ﬁrst-order transition). intensity is only one tenth of that measured at 4 K. Fig- ure 4b presents the dependence of the integrated PL We also studied the effect of the germanium deposi- intensity of the peak due to radiation from the Ge quan- tion rate on the optical properties of such structures. tum dots on the optical pump density, drawn on a logÐ Figure 5a shows PL spectra obtained at 4 K for samples m log scale. The data ﬁt the relation J = P , where J is the grown at rates VGe = 0.02 Å/s (sample A) and 0.2 Å/s PL intensity, P is the pump density, and the exponent m (sample B). As the growth rate decreases, the PL line is equal to 1.6 over a broad range of excitation densi- shifts considerably to shorter wavelengths. Figure 5b

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Si/Ge NANOSTRUCTURES FOR OPTOELECTRONICS APPLICATIONS 53

SiTO (a)

SI (0.90 eV)

WL1 (b) SiTO + O SiTA

A LI1(0.87 eV) Slow growth speed

WL BE

PL intensity, arb. units 2 Si B LI2(0.83 eV) High growth speed 100 nm 0.8 0.9 1.0 1.1 Photon energy, eV

Fig. 5. (a) PL spectra obtained at 4 K for a Ge/Si multilayer structure with a 7-Å-thick Ge layer in each unit layer, which were grown at growth rates VGe = 0.02 (sample A) and 0.2 Å/s (sample B). The graph shows PL lines responsible for the radiation from the silicon matrix (SiTO, SiTA, SiTO + O), the wetting layer (WL), small islands (SI), and large islands (LI). (b) TEM image of a cross section of the samples grown at different rates.

(a) d = 7 Å (b) Ge 0.95 dGe = 8 Å dGe = 9 Å 0.90

TO , eV

0.010 M Si 0.85 E

QDs 0.80

2.0 0.005 1.5 Intensity, arb. units 1.0

, arb. units 0.5 J 0 0 0.8 0.9 1.0 1.1 1.2 1.3 0 10 20 30 40 Photon energy, eV Sb exposition δ, s

Fig. 6. (a) PL spectra obtained at room temperature for Ge/Si multilayer structures with different Ge layer thicknesses in each unit layer, VGe = 0.15 Å/s; (b) position of the PL peak (EM) and radiation intensity J plotted vs surface hold time under the Sb ﬂow. displays TEM images of a cross section of these sam- shaped. The TEM surface images of the sample grown ples, which show that the germanium islands obtained at a low rate exhibit islands of two groups with different at smaller growth rates are lower and that in the initial dimensions. These groups provide different contribu- layers of the structure three-dimensional islands do not tions to the total PL (denoted in Fig. 5a by SI and LI for form at all. The germanium island thickness as esti- the small and large islands, respectively). At room tem- mated from these photomicrographs is 1Ð2 nm for the perature, however, the PL intensity of the islands grown low growth rate and 3Ð5 nm for the high growth rate. at a low rate drops rapidly. The WL peaks, which are The islands grown at different deposition rates likewise due to the radiation from the wetting layer, also lie at differ in shape; indeed, the low-rate islands are ﬂatter, different spectral positions, which is consistent with the while those grown at the higher rate are pyramid- assumption that smoothing of the surface is energeti-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 54 EGOROV et al.

EAe a change in the conduction band proﬁle of the Si spacer at the Si/Ge interface, as was the case in [13].

Ec The dependence of the optical properties of the samples consisting of Ge layers of the optimum thickness of 8 Å deposited at VGe = 0.15 Å/s on the doping level is shown graphically in Fig. 6b. The PL intensity is the strongest for the sample whose surface was maintained under a Sb flux for 20 s after deposition of each Ge PL layer. The PL peak is red-shifted as the hold time is increased to 20 s; then, after the maximum wavelength Buffer of 1.6 µm has been reached, the peak undergoes a blue shift. Note that, in structures with the Ge thickness in each layer differing from the optimum 8 Å, one can Cap achieve efficient PL by properly choosing the other growth parameters, namely, the germanium deposition rate and the doping level. E v Summing up the above experimental studies of the effect of the doping level, the amount of deposited ger- EAh manium in each layer of the structure, and its deposition rate on the optical and structural properties, we propose the following interpretation of the superlinear dependence of integrated PL intensity on excitation density. We believe that this dependence can be readily understood under the assumption that the electron wave functions overlap with the formation of a miniband in Fig. 7. Band diagram of a multilayer Ge/Si structure (schematic). the growth direction whereas the holes remain localized in the quantum wells formed by Ge inclusions. The corresponding band diagram is shown schematically in cally more favorable at low growth rates, as observed Fig. 7. Note the band bending near the upper layers of earlier for the InAs/GaAs system [12]. the structure, which appears because of the antimony atom segregation. One may conceive here two versions: Figure 6a presents room-temperature PL spectra of (a) if the miniband penetrates into the surrounding sili- Si/Ge multilayer structures with different Ge thick- con matrix, partial ejection of carriers into the matrix nesses in each unit layer of the superlattice. The Ge will make the PL intensity relatively weak, and (b) if deposition rate used in these experiments was 0.15 Å/s. the miniband is isolated from the Si matrix (as shown The PL intensity is obviously maximum in the case in Fig. 7), the PL intensity will be high and the expo- where the Ge thickness was 8 Å in each layer of the nent m will become greater than unity as a result of the structure and then decreases considerably with either formation of a heterojunction of the first type and of the an increasing or decreasing amount of deposited Ge. corresponding increase in the exciton oscillator Thus, there is an optimum thickness of the germanium strength. The band edge bending needed for this situa- layer needed to attain strong PL which depends on tion to be realized is provided by the corresponding Sb other growth parameters, for instance, the germanium doping level, which affects the miniband formation deposition rate. and, in the final count, the optical properties of Si/Ge multilayer quantum-well structures in a dominant way. One of the goals of our growth experiments consisted in studying the effect of antimony doping on the electronic and optical properties of the structure. The 4. CONCLUSIONS PL measurements performed on samples differing in the doping level revealed that the Sb concentration sub- Thus, we have demonstrated the possibility of stantially influences the optical properties of the sam- obtaining intense luminescence at room temperature ples. The PL is the strongest at a comparatively low near the 1.55-µm wavelength, which is of considerable doping, which is estimated from secondary ion mass importance for the development of long-distance fiber spectrometry data as n ~ 1017 cmÐ3. Both an increase communications. The radiation intensity grows super- and a decrease in the doping level bring about a drop in linearly with increasing pump density with the nonlin- the radiation intensity by a few times. At the highest earity exponent m = 1.6 within a broad range of pump doping levels [n ~ (5Ð7) × 1018 cmÐ3] attainable by densities. The proposed approach to the creation of an MBE at the substrate temperatures used, the PL peak active region appears promising for the development of shifts toward higher energies. This effect may be due to silicon-based light emitting diodes.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 Si/Ge NANOSTRUCTURES FOR OPTOELECTRONICS APPLICATIONS 55

ACKNOWLEDGMENTS 6. G. É. Cirlin, P. Verner, U. Gösele, et al., Pis’ma Zh. Tekh. Fiz. 27 (1), 31 (2001) [Tech. Phys. Lett. 27, 14 (2001)]. This study was supported in part by the Ministry of 7. G. E. Cirlin, V. A. Egorov, B. V. Volovik, et al., Nano- Industry, Science, and Technology of the Russian Fed- technology 12, 417 (2001). eration. One of the authors (G. É. C.) expresses warm gratitude to the Alexander von Humboldt Stiftung. 8. N. D. Zakharov, P. Werner, U. Gösele, et al., Mater. Sci. Eng. B 87, 92 (2001). 9. S. S. Mikhrin, A. E. Zhukov, A. R. Kovsh, et al., Semi- REFERENCES conductors 34, 119 (2000). 10. A. G. Makarov, N. N. Ledentsov, A. F. Tsatsul’nikov, 1. S. F. Fang, K. Adomi, S. Iyer, et al., J. Appl. Phys. 68, R31 (1990). et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 37 (2), 219 (2003) [Semiconductors 37, 210 (2003)]. 2. N. N. Ledentsov, in Proceedings of the 23rd Interna- tional Conference on the Physics of Semiconductors, Ed. 11. J. Wang, G. L. Jin, Z. M. Jiang, et al., Appl. Phys. Lett. by M. Schefﬂer and R. Zimmermann (World Sci., Sin- 78, 1763 (2001). gapore, 1996), Vol. 1, p. 19. 12. G. E. Cirlin, V. N. Petrov, A. O. Golubok, et al., Surf. Sci. 377Ð379, 895 (1997). 3. N. D. Zakharov, P. Werner, U. Gösele, et al., Appl. Phys. Lett. 76, 2677 (2000). 13. A. V. Dvurechenskiœ and A. I. Yakimov, Fiz. Tekh. Polu- provodn. (St. Petersburg) 35 (9), 1143 (2001) [Semicon- 4. S. Coffa, G. Franzo, and F. Priolo, Appl. Phys. Lett. 69, ductors 35, 1095 (2001)]. 2077 (1996). 5. L. Colace, G. Masini, G. Asanto, et al., Appl. Phys. Lett. 76, 1231 (2000). Translated by G. Skrebtsov

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Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 5Ð9. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 10Ð14. Original Russian Text Copyright © 2004 by Bresler, Gusev, Zakharchenya, Yassievich.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Electroluminescence Efficiency of Silicon Diodes M. S. Bresler, O. B. Gusev, B. P. Zakharchenya, and I. N. Yassievich Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia e-mail: [email protected]

Abstract—The intrinsic electroluminescence (EL) of a silicon light-emitting diode with a forward-biased pÐn junction is studied. The substantial enhancement of the integrated EL intensity observed with the temperature increasing from the liquid-nitrogen to room-temperature level, which is paralleled by an increase in the EL decay time when the current through the diode is terminated, indicates thermal suppression of the nonradiative recombination channel associated with deep traps. A simple model developed by us for the radiative processes occurring in a pÐn junction offers an interpretation for all the experimental data obtained. It is shown that the internal quantum efﬁciency of the EL may reach a level of a few percent under optimal doping of the diode p and n regions. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION from liquid-nitrogen temperature to room temperature, Room-temperature electroluminescence (EL) of sil- which was observed both by us and in [7]. We also icon is a topic of considerable current interest. Silicon determined the optimal parameters of the pÐn junction is a material with application potential in optoelectron- necessary to attain the maximum possible internal ics and is compatible with standard integrated circuit quantum efficiency of edge EL and the highest modula- technology, including ultralarge-scale integration tion frequency. (ULSI). Currently, silicon optoelectronics are developing in three directions, namely, (i) the application of sil- 2. EXPERIMENTAL RESULTS icon-based quantum structures [1Ð3], (ii) the introduction of rare earth impurities [4, 5], and (iii) the use of We used a standard alloyed silicon diode, with part new approaches to the investigation of the edge lumi- of its metal casing removed to couple out the radiation. nescence itself [6, 7]. Despite considerable progress The donor concentration in the n-type substrate was having been reached recently in the first two areas, the ~1 × 1015 cmÐ3. The acceptor concentration in the p problem of developing efficient silicon-based optoelec- layer was 5 × 1019 cmÐ3. These parameters are typical of tronic devices remains unsolved. This is probably why a conventional abrupt pÐn junction. In the region 77Ð researchers have again resumed investigation of the 300 K, all donors and acceptors are ionized; as a result, intrinsic luminescence of silicon in an attempt to the concentrations of the electrons and holes are equal increase the external quantum efficiency of the lumi- to those of the donors and acceptors, respectively. The nescent emission of a light-emitting structure [6] or to IÐV characteristics of our light-emitting diode mea- optimize the pÐn junction itself with the purpose of sured at liquid-nitrogen temperature and room temper- attaining the maximum possible intensity of intrinsic ature had the usual pattern (Fig. 1). The intrinsic silicon silicon emission [7]. It is maintained [7] that the dislo- EL was observed in the interval from liquid-nitrogen cation loops forming in the course of boron implanta- temperature to room temperature with current pulses tion favor an increase in the internal EL quantum effi- through the diode of up to 100 mA. The radiation was ciency at room temperature. Unfortunately, the collected from the diode side surface and directed into reported experimental data leave room for doubt in this a grating spectrometer equipped with a cooled germa- respect. nium photodetector. The EL decay time after termina- The present communication reports the first obser- tion of the diode current was measured using a digital vation and study of the edge EL of a forward-biased oscillograph. The time resolution of the measuring cir- alloyed silicon diode. Our experimental data are close cuit, limited by the germanium photodetector response, to those quoted in [7], where the pÐn structure was pre- was 5 µs. pared by implanting boron into an n-type substrate. We Figure 2 shows EL spectra of our light-emitting developed a simple model of the recombination pro- diode structure for temperatures of 77 and 300 K cesses occurring in a forward-biased pÐn junction. This obtained with a forward-biased pÐn junction. Practi- model is capable of accounting for the totality of our cally all of the intrinsic silicon EL radiation formed at experimental data, including the increase in the EL liquid-nitrogen temperature is due to free-exciton anni- intensity with temperature in the interval extending hilation, the line at 1.13 µm originating from recombi-

6 BRESLER et al.

60 14

40 10 1 12 20 6 2

Current, mA 0

EL intensity, arb. units 2 0 –20 0.95 1.05 1.15 1.25 1.35 –2 –1 0 1 2 Wavelength, µm Voltage, V Fig. 2. EL spectra of a silicon diode structure obtained at T Fig. 1. IÐV characteristics of the diode at T equal to (1) 300 equal to (1) 300 and (2) 77 K with a dc current of 20 mA and (2) 77 K. through the diode.

20 4 2 15 3

10 2 1

1 5 EL intensity, arb. units Integrated EL, arb. units 0 100 150 200 250 300 350 0 20 40 60 80 100 T, K Current, mA

Fig. 3. Integrated edge EL intensity plotted vs temperature. Fig. 4. Edge EL intensity of the diode structure plotted vs. Points are experimental data. The current through the struc- current through the pÐn junction for T equal to (1) 100 and ture is 20 mA. (2) 300 K. nation involving the emission of one transverse optical tion of the current pulse was less than 5 µs (the time res- phonon, and the 1.18-µm line originating from that olution of the measuring circuit) at 80 K and was 20 µs with the emission of two phonons. At room tempera- at room temperature. The external quantum efﬁciency ture, we observed a slight shift of the EL line maximum of our structure reached a level on the order of 10Ð4. relative to its position at liquid-nitrogen temperature. Interestingly, our experimental data practically This shift is less than the temperature-induced narrow- coincide with the results reported in [7]. The latter were ing of the silicon band gap and is accounted for by the obtained on a pÐn junction prepared by implanting fact that the edge luminescence spectrum at room tem- boron into an n-type phosphorus-doped substrate. perature consists of nearly equal contributions due to the recombination of free carriers with excitons. No other luminescence lines were observed in the wave- 3. RESULTS AND DISCUSSION length interval from 1.0 to 1.7 µm. To interpret the experimental results obtained, we Figure 3 plots the dependence of the integrated used the conventional model of a forward-biased abrupt intrinsic silicon EL intensity on temperature obtained pÐn junction. If the thickness of the depleted layer is by passing a dc current through the pÐn junction. This less than the carrier diffusion length, no recombination dependence is seen to have a linear section and a max- takes place in the depleted layer. The rate of radiative imum at a temperature close to room temperature, recombination in the n layer of the structure can be which is in agreement with the data from [7]. The written as dependence of the integrated intensity of the intrinsic qV xlÐ n EL on current was practically linear at both liquid------Ð------kT Lp nitrogen temperature and room temperature (Fig. 4). R ==r n ∆prn p e Ð 1 e , (1) The decay time of the EL intensity following termina- n r n r n n

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

ELECTROLUMINESCENCE EFFICIENCY OF SILICON DIODES 7 where r is the radiative recombination coefﬁcient, n is r n –4 2 the concentration of majority carriers (electrons in the 10 ∆ n region), p is the concentration of the holes injected 10–5 into the n region, pn is the concentration of minority 1 10–6 carriers (holes) in the n region of the pÐn junction at , s p thermodynamic equilibrium, V is the voltage across the τ

, –7

n 10 pÐn junction, Lp is the hole diffusion length in the n τ –8 region, ln is the depleted-layer thickness in the n region, 10 and x is the distance from the boundary of the pÐn junc- –9 tion. 10 We performed measurements with dc current passed through the pÐn junction. Therefore, it is convenient to 1015 1016 1017 1018 1019 1020 –3 substitute the current expressed through the IÐV charac- nn, pp, cm teristic of the pÐn junction into Eq. (1): qV qV Fig. 5. Minority carrier lifetime vs. majority carrier concen------tration plots at T = 300 K [8]: (1) τ and (2) τ . kT ≡ Dnn p D p pn kT n p jj= 0e Ð 1 q------+ ------e Ð 1 , (2) Ln L p where Ln is the electron diffusion length in the p region; under study. Using the above estimates and the majority 4 Dn and Dp are the diffusion coefficients of electrons and carrier concentration ratio pn/np ~ 10 , we find from holes, respectively; and np is the equilibrium concentra- Eq. (3) tion of the minority carriers (electrons) in the p region. D n D p Ð1 Integration of Eq. (1) over x yields the photon flux ≈ j n p p n In rrnn pn L p---------+ ------density emitted from the n region in the direction per- q Ln L p pendicular to the plane of the pÐn junction: (6) 2 j j = r n p L ------= r n τ ---. j D p D n Ð1 r n n p qD p r n pq I = r n p L ------p n + ------n -p . (3) p n n r n n pqL L p n As seen from Eq. (6), the integrated EL intensity is In the same way, one can find the photon flux density linear in current density (in accordance with the data in emitted from the p region: Fig. 4) and its temperature dependence is determined Ð1 by the temperature behavior of the hole lifetime in the j D p pn Dnn p n region and by that of the radiative recombination I p = rrn p p p Ln---------+ ------. (4) q L p Ln coefficient rr.

Because nnpn = ppnp, the ratio of the EL intensities It was shown in [10] that the radiative recombina- emitted from the two sides of the pÐn junction can be tion coefficient for indirect-gap radiative transitions of written as excitons and free carriers scales with increasing temperature as I L D τ ----n ==-----p ------p -,p (5) τ E E Θ I p Ln Dn n ∝ Ex x x  rr ------1+ 2 ------exp------coth------, (7) which means that the EL intensity ratio for the n and p kT kT kT 2T regions is determined only by the diffusion length ratio Θ of the minority carriers injected into these regions. where Ex is the exciton binding energy and is the Figure 5 displays the averaged lifetimes of electrons Debye temperature of the transverse optical phonon. and holes in the p and n regions, respectively, taken Because of the high Debye temperature, the last factor from [8]. For our structure, the lifetime of holes in the in Eq. (7) is practically temperature-independent and equal to unity. The first term in the brackets in Eq. (7) n region is 2 × 10Ð5 s (for a donor concentration of 15 Ð3 describes the band-to-band recombination of free carri- 10 cm ), whereas for electrons in the p region (for an ers (with due allowance made for the Coulomb interac- 19 Ð3 acceptor concentration of 5 × 10 cm ) the corre- tion between them), whereas the second term corresponding time is 10Ð8 s. To estimate the diffusion coef- sponds to the free-exciton recombination. Thus, the ficients, we made use of the data on mobilities from [9]. temperature dependence of the radiative recombination The diffusion coefficient of holes for the doping levels coefficient is governed primarily by the decrease in the corresponding to our pÐn junction is about four times free-exciton concentration. It is this temperature- greater than that of the electrons. Therefore, the diffu- induced decrease in the radiative recombination coeffi- sion length of holes Lp is a few tens of times larger than cient that accounts for the usually observed decrease in that of electrons, Ln. Accordingly, the n region provides the photoluminescence intensity with increasing tem- the major contribution to the edge EL in the structure perature.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 8 BRESLER et al. However, our experimental data indicate that the EL rier lifetime slows down, to be subsequently replaced τ intensity and its decay time after the current pulse is by a decrease in p. turned off increase with temperature. To explain these τ Thus, we associate the observed growth in the EL observations, one has to assume that the hole lifetime p intensity with temperature with the increasing effective increases with temperature faster than the radiative lifetime of the injected holes. As follows from our con- recombination coefficient rr decreases. sideration, this growth in intensity implies the existence We believe that the n region of the diode under study of deep nonradiative recombination centers in the sam- contains a certain concentration of traps acting as ple, i.e., insufficient quality of the diode emitter part. recombination centers [this concentration should be less than that of the majority carriers (electrons)]. On the other hand, data obtained on the photoluminescence 4. OPTIMAL LIGHT-EMITTING DIODE of n-type samples with the same doping level show PARAMETERS FOR THE EDGE their luminescence intensity to decrease with tempera- ELECTROLUMINESCENCE FROM SILICON ture, which means that they do not contain such recom- So far, we have studied edge EL in silicon by using bination centers as the n region of the diode. We assume standard-type light-emitting structures, i.e., with a that the traps in the diode n region arise because the lightly doped n region and a heavily doped p-type defects forming under heavy doping of the p region region. This technology is appropriate for diodes penetrate into the n region. Note that the defect penetra- employed as current rectifiers, because they should tion depth into the p region should in this case be large have a high reverse breakdown voltage. At the same enough, at least on the order of the diffusion length of time, a good backward branch of the IÐV characteristic τ 1/2 ≈ × Ð5 1/2 ≈ the minority carriers Lp = (Dp p) (3 10 ) is of no use for a light-emitting structure and, therefore, 60 µm. one can vary the doping levels of the n and p regions so It is quite possible that the hole lifetime τ is gov- as to reach the maximum efficiency of the edge EL in p the light-emitting structure. We carried out a calcula- erned by the nonradiative trapping of holes by deep tion of the optimum diode structure that would provide attracting centers. In this case, the trapping process can the maximum possible quantum efficiency of intrinsic be divided into two stages. In the first stage, the holes EL. The internal quantum efficiency can be written in are trapped into higher lying Coulomb states, to drop the form subsequently down through the densely spaced energy spectrum of these states (the cascade mechanism of hν()I + I hν()j/q r A η = ------n p- ≡ ------r I , (9) trapping). However, the dense spectrum of high excited jV jV states extends, as a rule, only to a depth of the order of the shallow-center Bohr binding energy, i.e., about 45Ð where the numerator describes the edge EL power and 50 meV in silicon. This spectrum is separated from the the denominator is the electrical power consumed by ≅ ν ≅ ground state by a large energy gap, and as a result the the diode. Assuming V Eg/q and recalling that h second trapping stage (transition to the ground state) Eg, we can recast the expression for the internal quan- requires a high energy transfer and can occur in a non- tum efficiency as radiative manner only as a multiphonon process, with a considerably lower probability. Therefore, a trapped D p D n Ð1 η = r A ≡ r n p ()L + L ------p -p + ------n -n . (10) carrier can reside for a long enough time in the last r I r n p n p L L excited state that one may consider this state metastable p n and describe the total recombination process by the This relation has a very simple physical meaning; two-level center model. The recombination process namely, if, for instance, the main contribution to the EL involving a metastable level with a characteristic comes from the p region of the pÐn junction, the inter- energy Et is discussed in [8]. nal quantum efficiency is simply the ratio of the total As the temperature increases, the carriers residing in lifetime of minority carriers (electrons) to the radiative the metastable state are more likely to be ejected back lifetime: into the band than go to the ground state. In this case, τ the effective minority carrier lifetime begins to grow η τ ≡ n = rr p p n ----τ . (11) exponentially with temperature: r τ ∝ exp()ÐE /kT . (8) Figure 6 plots the internal quantum efficiency calcu- T t lated by means of Eq. (10) for various doping levels of The carrier lifetime increases up to the point where the pÐn junction. The value used for the radiative Ð14 3 Ð1 thermal activation becomes sufficiently strong and the recombination coefficient, rr = 10 cm s , was taken multiphonon-assisted carrier transition from the first from [10]. Interestingly, a decrease in the mobility, excited to the ground state of the recombination center which is proposed in [7] as a means to attain a higher is more likely to occur than the reverse ejection into the internal quantum efficiency, can bring about, as is evi- band. In this temperature region, the increase in the car- dent from Eq. (11), a decrease in the EL intensity only.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 ELECTROLUMINESCENCE EFFICIENCY OF SILICON DIODES 9

dopings, the quantum efﬁciency drops as a result of the 4 3 enhanced Auger recombination of the minority carriers, while lower doping levels bring about a decrease in the 3 2 radiative recombination probability proportional to the product nnpp. Because high doping levels are usually accompanied by the formation of defects in high con- 2 IQE, % 4 centrations, a carrier concentration in the p region of about 1017 cmÐ3 would probably be more favorable. As 1 follows from Fig. 6, an optimally designed light-emit- 1 ting diode with an n-region concentration of 1017 cmÐ3 0 and a concentration in the p region of 1017 cmÐ3 could 1015 1016 1017 1018 1019 1020 have an internal quantum efﬁciency of up to 3% at a Concentration, cm–3 modulation frequency of 50 kHz.

Fig. 6. Internal quantum efficiency (IQE) vs. electron concentration nn in the n region of the pÐn junction plotted for ACKNOWLEDGMENTS various values of the hole concentration pp in the p region: This study was supported by the Russian Founda- (1) 1016, (2) 1017, (3) 1018, and (4) 1019 cmÐ3. tion for Basic Research, the Netherlands scientific research foundation (NWO), the Ministry of Industry, Science, and Technology of the Russian Federation, Our estimates based on literature data suggest that and the RAS Physical Sciences Division program the light-emitting structures used currently to study the “New Materials and Structures.” intrinsic silicon EL are far from being optimal. A diode 19 Ð3 × with concentrations nn = 10 cm and pp = 1.4 1016 cmÐ3 was reported in [6] to have an internal quan- REFERENCES tum efficiency of about 1%, which is in agreement with 1. Z. H. Lu, D. J. Lockwood, and J. M. Baribeau, Nature our calculations. By contrast, the structure studied in 378, 258 (1995). [7] and characterized by doping levels of 1019 and 2. K. D. Hirschman, L. Tsybeskov, S. P. Duttagupta, and 1015 cmÐ3 for the p and n regions, respectively, could be P. M. Fauchet, Nature 384, 338 (1996). expected to have a quantum efficiency of the order of 3. G. Franzò, A. Irrera, E. C. Moreira, et al., Appl. Phys. A 0.01% only. The EL quantum efficiency of our diode is 74 (1), 1 (2002). estimated to be exactly of this order of magnitude. 4. G. Franzò, F. Priolo, S. Coffa, et al., Appl. Phys. Lett. 64 (17), 2235 (1994). Note that the decay times of edge luminescence at 5. B. Zheng, J. Michel, F. Y. G. Ren, et al., Appl. Phys. Lett. room temperature measured in our study and reported 64 (21), 2842 (1994). µ in [7] practically coincide and are equal to 20 s, which 6. M. A. Green, J. Zhao, A. Wang, et al., Nature 412, 805 agrees with the data in Fig. 5. At the same time, the (2001). internal quantum efficiency obtained in [7] is approxi- 7. W. L. Ng, M. A. Lourenc, o, R. M. Gwilliam, et al., mately 0.5%, which is clearly at odds with our result. Nature 410, 192 (2001). We believe the reason for this discrepancy could be 8. V. N. Abakumov, V. I. Perel’, and I. N. Yassievich, Non- incorrect measurement of the quantum efficiency in [7]. radiative Recombination in Semiconductors (S.-Peterb. As seen from Fig. 6, the maximum quantum effi- Inst. Yad. Fiz. Ross. Akad. Nauk, St. Petersburg, 1997). ciency of the recombination radiation is attained when 9. C. Jacoboni, C. Canali, G. Ottaviani, and A. Alberigi the n region is doped to 1019 cmÐ3 and the p region is Quaranta, Solid-State Electron. 20 (2), 77 (1977). 18 Ð3 10. H. Schlangenotto, H. Maeder, and W. Gerlach, Phys. doped to 10 cm . In this case, the major contribution Status Solidi A 21 (2), 357 (1974). to the luminescence is provided by the p region and the comparatively high quantum efficiency is due to the large electron diffusion length. For higher n-region Translated by G. Skrebtsov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 56Ð59. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 60Ð62. Original Russian Text Copyright © 2004 by Dvurechenskiœ, Yakimov, Nenashev, Zinov’eva. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Ge/Si Quantum Dots in External Electric and Magnetic Fields A. V. Dvurechenskiœ, A. I. Yakimov, A. V. Nenashev, and A. F. Zinov’eva Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia e-mail: [email protected]

Abstract—Electric ﬁeld-induced splitting of the lines of exciton optical transitions into two peaks is observed for Ge/Si structures with quantum dots (QDs). With increasing ﬁeld, one of the peaks is displaced to higher optical transition energies (blue shift), whereas the other peack is shifted to lower energies (red shift). The results are explained in terms of the formation of electronÐhole dipoles of two types differing in the direction of the dipole moment; these dipoles arise due to the localization of one electron at the apex of the Ge pyramid and of the other electron under the base of the pyramid. By using the tight-binding method, the principal values of the g factor for the hole states in Ge/Si quantum dots are determined. It is shown that the g factor is strongly anisotropic, with the anisotropy becoming smaller with decreasing QD size. The physical reason for the dependence of the g factor on quantum-dot size is the fact that the contributions from the states with different angular- momentum projections to the total wave function change with the QD size. Calculations show that, with decreasing QD size, the contribution from heavy-hole states with the angular-momentum projections ±3/2 decreases, while the contributions from light-hole states and from states of the spin-split-off band with the angular-momentum projections ±1/2 increase. © 2004 MAIK “Nauka/Interperiodica”.

1. QUANTUM DOTS tocurrent spectroscopy. Two conditions have to be sat- IN AN ELECTRIC FIELD isfied for experimental observation of the Stark effect. First, the size of Ge nanocrystals must be sufficiently Application of an electric field to a system of quan- small for the spectrum of electronic states to be dis- tum dots (QDs) results in energy-level shifts in optical crete. The other condition is that the spatial electronÐ transitions (the Stark effect in quantum-confinement hole separation must be such that the electric dipole systems; see, e.g., [1, 2]). Most studies of the Stark moments are sufficiently large. To satisfy these condi- effect have been performed on type-1 (InAs/GaAs) het- tions, the method of heteroepitaxy of Ge on Si with the erostructures. The red shift of optical transition ener- addition of oxygen before Ge deposition was devel- gies in an electric field was observed in those studies. In oped in [4]. This method provides the possibility of type-2 heterostructures, electrons and holes are local- forming hemispherical Ge islands with a size of the ized on different sides of the heterointerface and, once base of the nanocluster of about 6 nm and a height of their spatial separation is sufficiently large, one may 3Ð4 nm. expect a strong manifestation of the Stark effect. The electric field ranged up to 100 kV/cm. For low The Ge/Si structures with QDs form type-2 hetero- electric fields, a symmetric photocurrent peak is junctions. When an electronÐhole pair is photogener- observed at a photon energy of about 1040 meV for the ated, the hole is localized in Ge, whereas the electron is structures studied; this peak is attributed to indirect located in the potential well formed in Si near the vertex excitonic transitions between the hole ground state in of the Ge pyramid. Such an excitation is called the spa- Ge and the ground state of an electron localized in Si tially indirect exciton. If a biexciton is formed, holes near the Ge/Si heterointerface. An electronÐhole pair still remain localized in Ge; however, for the second generated by photoexcitation dissociates into its com- electron, localization under the base of the Ge pyramid ponents due to thermal fluctuations (the measurements appears to be energetically more favorable [3]. Such a are made at room temperature) and contributes to the geometrical configuration results in opposite orienta- photocurrent. The width of the photocurrent peak tions of the dipoles with respect to the electric field increases with electric field, and, finally, the peak splits directed along the symmetry axis of the Ge pyramid into two peaks. As the electric field is increased fur- (along the growth axis; Fig. 1). ther, the energy positions of these two peaks are dis- Interband optical transitions in Ge/Si systems with placed in opposite directions (the red and blue shifts; QDs in an electric field were studied in [4] using pho- Fig. 2).

Ge/Si QUANTUM DOTS IN EXTERNAL ELECTRIC AND MAGNETIC FIELDS 57

These results have a sufficiently simple qualitative explanation in terms of the conception of the two (a) Ec dipoles that are formed on Ge quantum dots and have Electron Electron opposite directions with respect to the applied electric Si Si field. For one of the dipoles, the external field increases Ge the overlap of the wave functions of the electron and the hole and, therefore, increases the exciton binding Eυ energy and gives rise to a blue shift in the photocurrent Hole spectrum. For the dipole of the opposite direction, the overlap of the wave functions decreases, thereby producing a decrease in the exciton binding energy and a red shift of the photocurrent peak. Ge dot Perturbation-theory estimations of the spatial sepa- Apex Base rations between electrons and holes and the experimen- p+-type tal data on the electric-field dependence of the photo- Electric field current peaks yield values that agree with the geometrical QD configuration obtained by electron microscopic studies. Thigh (b) Tlow 2. QUANTUM DOTS IN A MAGNETIC FIELD + A splitting of discrete levels of an atom or a QD n -type (artificial atom) in a magnetic field (Zeeman effect) is Growth direction z determined by the magnetic-moment projection on the field direction. In turn, the magnetic moment is related to the angular momentum by the Lande factor, which actually determines the value of the splitting of discrete Fig. 1. (a) Band structure of the Ge/Si type-2 heterostruc- levels. The Lande splitting factor for a free electron ture along the growth direction passing through the center ≈ ± of symmetry of a Ge quantum dot and (b) band structure of ( 2) describes the interaction of the electronic 1/2 the pÐiÐn diode under reverse bias (schematic). spin states with an external magnetic field. In solids, the g factor is substantially different from the g factor for free electrons due to the interaction with the lattice potential. With lowering the dimensionality of the system from the three-dimensional (3D) to the two-dimen- 40 sional (2D) case and further, the quantum-confinement 5.5 V T effects also change the carrier g factor. For example, for Tlow high electrons in low-dimensional systems, the quantization results in substantial renormalization of the value of the 30 g factor [5] and in its strong anisotropy [6]. The Lande factor contains quantitative information on the change 5.0 V in the semiconductor band structure with decreasing 20 dimensionality and has been studied in numerous 4.8 V experimental and theoretical papers. For electron 4.3 V states, there are papers in which the g factor of an elec- Responsivity, mA/W 10 tron in a quantum well or a QD was calculated [7]. For hole states, the Zeeman effect has been studied the- 0.2 V oretically and experimentally for structures with quan- 0 V 0 tum wells. 900 1000 1100 1200 In the case of QDs, the existence of confinement Photon energy, meV potential not only in the growth direction (as in the case of 2D structures) but also an equally strong quantization in the lateral direction should produce a significant Fig. 2. Dependence of photocurrent spectra on reverse bias. renormalization of the g factor for hole states. In addition, for QDs in strained heterostructures, nonhomoge- ε ε neity of strains inside quantum dots also strongly xz, and yz (here, z is the growth direction and x and y affects the g factor. Comparison of a quantum dot and a lie in the base plane of the pyramid), resulting in mixing quantum well, both grown in the 〈100〉 direction, shows of the states of light and heavy holes and of the states of ε that in the latter structure there are no shear strains xy, the spin-split-off band [8]. Such strains exist in QDs.

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58 DVURECHENSKIŒ et al.

90 tribution from the states with the angular-momentum ± projections Jz = 3/2 on the symmetry axis of the Ge 88 island (Fig. 3). 86 The probability of Zeeman transitions is directly related to the character of the wave function. For the 84 ± || states with Jz = 3/2 in the magnetic ﬁeld H z, induced transitions between the Zeeman sublevels with J = 82 z +3/2 and Jz = Ð3/2 are forbidden by the selection rules; for allowed transitions, the condition ∆J = ±1 must be

-state contribution, % 80 z 〉 ± satisfied. The admixture of the Jz = 1/2 states facili- 3/2 | 78 tates the transitions between Zeeman sublevels of the 76 ground state in the Ge island; therefore, with decreas- 0 5 10 15 20 25 30 35 ing island size, the suppression of Zeeman transitions Island size l, nm becomes weaker. In the case of a dc magnetic field H || z, the micro- ± Fig. 3. Contribution from the Jz = 3/2 states to the hole wave field Hω lies in the plane of the QD layer and the ground state as a function of the lateral size of a germanium Zeeman transition probability is proportional to the island 1.5 nm in height. square of the matrix element of the magnetic moment component µ in the direction of the microwave field. In Thus, for quantum dots, quantization in all three direc- the special case of the microwave field Hω directed along [110], the particle magnetic moment component tions and nonhomogeneity of strains should signifi- µ cantly modify the g factor of hole states due to the mix- is proportional to the principal value gxx of the g ten- ing of the energy bands. sor and, for Hω || [110 ], the particle-magnetic-moment µ In [9], a method is suggested for calculating the g component is proportional to gyy. Accordingly, the factor for hole states in quantum dots by using the tight- transition probabilities are determined by the squares of binding approach. This method takes into account a 2 these components of the g tensor, g (Hω || [110]) and specific form of the quantizing potential (not necessar- xx 2 || ily described by an analytical function) and can be gyy (Hω [110 ]). applied to calculate the g factor for QDs of any shape and of arbitrarily small size. This method can also be In the case of a dc magnetic field H ⊥ z, the mag- applied to electronic states in QDs. netic-moment component µ lies in the plane perpendicular to the base plane and, in the special case of the If the Zeeman splitting of levels is small compared microwave field Hω directed along [100], it is propor- to the size-quantization energy, then the g factor depends only on the direction of the magnetic field and tional to the principal value gzz of the g tensor. The tran- 2 can be written in the first-order perturbation theory as sition probability in this case is proportional to gzz . For the obtained values of the g factor, the probabilities of 2 g = 2 〈|ψ nMˆ |〉ψ 2 +,〈|ψ nMˆ |〉ψ* induced transitions for the two directions of the mag- QD QD netic field (H || z and H ⊥ z) differ by a factor of approx- where n is a unit vector in the magnetic field direction, imately 100. ψ and ψ* are the wave functions of the level consid- ˆ ered, and MQD is the magnetic-moment operator for a ACKNOWLEDGMENTS hole. Calculations for a Ge/Si system with QDs show that This study was supported by the Russian Founda- the g factor of a hole in the ground state is strongly tion for Basic Research (project nos. 02-02-16020, anisotropic, with the longitudinal component g of the 03-02-16526), the program “Universities of Russia” zz (project no. UR.01.01.019), and INTAS (grant g factor being an order of magnitude larger than the no. 2001-0615). transverse components gxx and gyy. For example, for a typical Ge island with base size l = 15 nm and height h = 1.5 nm, the values of the g factor components are REFERENCES gzz = 12.28, gxx = 0.69, and gyy = 1.59. From the calculated dependence of the g factor on 1. J. A. Barker and E. P. O’Reilly, Phys. Rev. B 61, 13840 the size of Ge islands, it follows that the g-factor anisot- (2000). ropy increases with the island size. Such a behavior of 2. P. W. Fry, I. E. Itskevich, D. J. Mowbray, et al., Phys. the g factor is mainly determined by the increased con- Rev. Lett. 84, 733 (2000).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 Ge/Si QUANTUM DOTS IN EXTERNAL ELECTRIC AND MAGNETIC FIELDS 59

3. A. I. Yakimov, A. V. Dvurechenskiœ, and A. I. Nikiforov, 7. A. A. Kiselev, E. L. Ivchenko, and U. Rössler, Phys. Rev. Pis’ma Zh. Éksp. Teor. Fiz. 73 (10), 598 (2001) [JETP B 58, 16353 (1998). Lett. 73, 529 (2001)]. 8. G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced 4. A. I. Yakimov, A. V. Dvurechenskii, A. I. Nikiforov, Effects in Semiconductors (Nauka, Moscow, 1972; et al., Phys. Rev. B 67 (12), 125318 (2003). Wiley, New York, 1975). 5. M. Bayer, V. B. Timofeev, T. Gutbrod, et al., Phys. Rev. 9. A. V. Nenashev, A. V. Dvurechenskiœ, and A. F. Zi- B 52, R11623 (1995). nov’eva, Zh. Éksp. Teor. Fiz. 123 (2), 362 (2003) [JETP 96, 321 (2003)]. 6. V. K. Kalevich, B. P. Zakharchenya, and O. M. Fedorova, Fiz. Tverd. Tela (St. Petersburg) 37 (1), 283 (1995) [Phys. Solid State 37, 154 (1995)]. Translated by I. Zvyagin

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 60Ð63. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 63Ð66. Original Russian Text Copyright © 2004 by Vostokov, Krasil’nik, Lobanov, Novikov, Shaleev, Yablonskiœ. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Photoluminescence of Self-Assembled GeSi/Si(001) Nanoislands of Different Shapes N. V. Vostokov, Z. F. Krasil’nik, D. N. Lobanov, A. V. Novikov, M. V. Shaleev, and A. N. Yablonskiœ Institute of the Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected]

Abstract—The dependence of the photoluminescence spectra of structures with self-assembled GeSi/Si(001) islands on Ge deposition temperature was studied. The position of the island photoluminescence peak maximum was found to shift nonmonotonically with decreasing Ge deposition temperature. The blue shift of the island photoluminescence peak with the growth temperature decreasing from 600 to 550°C is assigned to the change in the island shape occurring in this temperature interval accompanied by a strong decrease in the average island height. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION deposited Ge. The surface morphology of the structures was studied with a Solver P4 atomic force microscope The formation of three-dimensional self-assembled (AFM). The PL spectra were measured with a BOMEM islands caused by the lattice misfit between Ge and Si DA3.36 Fourier spectrometer equipped with a cooled has been experimentally observed to occur on the + Si(001) surface within a broad range of Ge deposition InSb detector. An Ar laser (514.5 nm line) served for temperatures [1Ð3]. By properly varying the Ge depo- optical pumping. sition temperature, one can obtain both large nanoislands, >100 nm in the lateral dimension [1, 2], and 3. RESULTS AND DISCUSSION extremely small islands (quantum dots) whose maxi- Earlier studies of the growth of GeSi nanoislands mum size does not exceed 15Ð20 nm [2, 3]. The growth ≥ ° temperature affects not only the size of the islands but performed at Ge deposition temperatures Tg 600 C also their shape [1] and composition [4]. The dimen- showed [1Ð4] that, at an effective thickness of depos- sions of the islands and their shape and composition are ited Ge dGe = 7Ð8 MLs, the formations appearing on the the parameters that determine the position of the energy surface are of two types differing in shape and size, bands in nanoisland structures. The dependence of namely, pyramidal and dome-shaped islands. It was ≥ ° these parameters on growth temperature should give found in [4] that for Tg 600 C the growth of islands is rise to a substantial difference between the band dia- strongly affected by the formation of a GeSi alloy in the grams of structures with nanoislands grown at different islands, which is caused by Si diffusion into the islands temperatures, which, in turn, should influence their accelerated by the elastic strain fields generated by the optical properties. We report here on a study of the latter. AFM studies of these structures revealed that for growth and photoluminescence (PL) of structures with dGe = 7Ð8 MLs the dominant species is the dome- self-assembled GeSi/Si(001) islands grown within a shaped islands, which have a larger height and are broad Ge deposition temperature interval (460Ð700°C). larger in size in the growth plane as compared to the pyramidal islands (Fig. 1a). As Tg is lowered from 700 to 600°C, the islands decrease monotonically in size 2. EXPERIMENTAL TECHNIQUE (Fig. 1d) and their surface density increases (Fig. 1e). The structures under study were grown on Si(001) The growth in the island surface density is caused by a substrates from solid sources through molecular-beam slowing down of surface diffusion of atoms setting in as epitaxy. The structures intended for investigating the the temperature decreases. The decrease in the island surface morphology consisted of a Si buffer layer size with decreasing Tg is associated with suppression grown at 700°C and a Ge layer with an equivalent of the Si diffusion into the islands and an increase in the ≈ thickness dGe = 7Ð8 monolayers (MLs) (1 ML Ge content in the latter [4]. 0.14 nm) deposited within the temperature interval Tg = As the Ge deposition temperature decreases from 460Ð700°C. In structures designed for optical studies, a 600 to 550°C, the growth of self-assembled islands Si cap layer whose growth temperature coincided with undergoes a qualitative change (Fig. 1). Lowering Tg by the deposition temperature of Ge was grown on the as little as 50°C brings about an order-of-magnitude

PHOTOLUMINESCENCE OF SELF-ASSEMBLED GeSi/Si(001) 61

nm (a)nm (b)nm (c) 500 500 500 400 400 400 300 300 300 200 200 200

100 100 100

0 100 200 300 400 nm 0 100 200 300 400 nm 0 100 200 300 400 nm

(d)–2 (e) 1011 10 Dome-island Hut-island

1010

Island height, nm Hut-island Dome-island

1 9

Surface island density, cm 10 450 500 550 600 650 700 450 500 550 600 650 700 Ge growth temperature, °C Ge growth temperature, °C

Fig. 1. (aÐc) AFM surface photomicrographs of structures grown at 600, 550, and 460°C, respectively (image span 500 × 500 nm), and (d, e) plots of the average height of islands and their surface density vs Ge deposition temperature. The dashed lines in panels ° c and d separate the regions of existence of the hut- and dome-shaped islands and correspond to Tg = 580 C.

0.80 (a) Tg = 700°C (b) T = 4 K 0.78 650°C 0.76 600°C 0.74 550°C Hut Dome 0.72 500°C PL peak, eV 0.70 PL intensity, arb.units 460°C 0.68 0.5 0.6 0.7 0.8 0.9 1.0 450 500 550 600 650 700 Photon energy, eV Ge growth temperature, °C

Fig. 2. (a) PL spectra of structures with islands grown at different Ge deposition temperatures and (b) position of the island PL peak maximum plotted vs Tg. The PL spectra were measured at 4 K using an InSb detector.

≤ ° increase in the surface density of islands (Fig. 1e), with surface of the structures for Tg 550 C and dGe = 7Ð ° the island height decreasing about ﬁvefold (Fig. 1d). 8 MLs (Fig. 1b). As Tg is lowered from 550 to 460 C, The sharp change in the island parameters is connected the height of the hut islands decreases monotonically with the formation of so-called hut islands [5] (with a and their surface density increases (Fig. 1). At Tg = rectangular base extended in the 〈100〉 or 〈010〉 direc- 460°C, the hut islands are 0.7Ð1.0 nm high, their size in tion) on the surface (Fig. 1b). Islands of this type appear the growth plane becomes 15Ð30 nm, and their surface ° × 11 Ð2 at Tg = 580 C [6] (Fig. 1) and become dominant on the density is Ns = 2.5 10 cm (Fig. 1c).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

62 VOSTOKOV et al.

(a) (b) ∆ ∆ 2 ee 2 ee

Si Si Si Si h h Eυ Eυ Dome Hut island island

Fig. 3. Model of the indirect optical transition for (a) dome- and (b) hut-shaped islands (schematic). The positions of the valence band top and of 2∆ electron valleys in the islands and their neighborhood are speciﬁed. The arrows identify the indirect optical transition.

Studies of PL spectra of all our structures revealed a erface and, hence, to a decrease in the indirect optical broad PL peak in the low-energy part of the spectra transition energy [8] (Fig. 3a). (Fig. 2a). This PL peak is assigned to the indirect opti- The Eisl(Tg) dependence has a feature at Tg = 550Ð cal transition between the holes in the islands and elec- 600°C; more specifically, the island PL peak becomes trons located in Si at the type-II heterointerface with an blue-shifted by ~50 meV with Tg decreasing from 600 island [7]. A substantial part of the PL signal from the ° ≤ ° to 550 C (Fig. 2). Studies of island growth revealed that islands grown at Tg 650 C was shown in [8] to lie at it is in this Tg interval that the island morphology under- energies below the low-energy cutoff of the operating goes a substantial change (Fig. 1). As shown above, for range of a cooled Ge detector. To avoid modification of ° Tg > 580 C, the surface of the structures is dominated the island PL signal by the spectral response of the Ge by dome-shaped islands with a height greater than detector, we measured the PL spectra with a less sensi- 10 nm and for T < 580°C, by hut islands with a height tive cooled InSb detector with a cutoff at a longer wave- g of ≤2 nm (Fig. 1d). The sharp decrease in the island length. height brings about a substantial increase in the influ- A comparison of the PL spectra due to structures ence of size quantization on the hole energy level posi- grown at different Ge deposition temperatures showed tion in the islands. As a result, despite the increase in the valence-band offset at the Si-island heterointerface the position of the island PL peak maximum (Eisl) to depend nonmonotonically on T (Fig. 2). As in the case associated with the increase in Ge content in the islands g that occurs with decreasing T , the first size-quantiza- of island growth, the E (T ) relation can be divided g isl g tion level of the island holes shifts (is forced) toward the into two parts (Fig. 2b). Si valence band top (Fig. 3b); as a result, the optical ≥ ° transition energy in the islands increases and the PL In the first part, with Tg 600 C, Eisl decreases monotonically with decreasing growth temperature. As line exhibits the observed shift. the temperature decreases, the optical transition energy The monotonic decrease in Eisl with Tg decreasing in islands is affected by the following two major fac- from 550 to 460°C is assigned to suppression of varia- tors: a decrease of the islands in size and a change in tions in the island parameters as the islands become ≥ ° their composition. For Tg 600 C, the first factor overgrown. It is known that, as the Si cap layer grows, affects the optical transition energy in the islands only the Si content in the islands increases and their height ° weakly, because even at Tg = 600 C the uncapped decreases [9]. As the overgrowth temperature is low- dome-shaped islands are higher than 10 nm (Fig. 1d), ered from 500 to 390°C, these processes were shown to so the size quantization effects exert only a weak influ- become largely suppressed [10]. Thus, as the growth ence on the position of the first size-quantization level temperature decreases from 550 to 460°C, the height of of holes in the islands. As a result, the hole energy level the capped islands increases, as does their average Ge in islands is located close to the valence band top content. Both these processes bring about a decrease in (Fig. 3a). The position of the island PL peak is affected the optical transition energy in the islands (Fig. 3b) and, primarily by the dependence of the island composition accordingly, a red shift of the island PL peak. on growth temperature. The red shift of the island PL peak should be assigned to suppression of Si diffusion ACKNOWLEDGMENTS into the islands occurring with decreasing growth temperature and, accordingly, to an increase in the Ge con- This study was supported by the Russian Founda- tent in the islands [4], which gives rise to an increase in tion for Basic Research (project no. 02-02-16792), the valence-band offset at the siliconÐisland heteroint- INTAS NANO (project no. 01-444), and programs of

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 PHOTOLUMINESCENCE OF SELF-ASSEMBLED GeSi/Si(001) 63 the Ministry of Industry, Science, and Technology of 6. O. G. Schmidt, C. Lange, and K. Eberl, Phys. Status the Russian Federation. Solidi B 215, 319 (1999). 7. V. Ya. Aleshkin, N. A. Bekin, N. G. Kalugin, et al., Pis’ma Zh. Éksp. Teor. Fiz. 67, 46 (1998) [JETP Lett. 67, REFERENCES 48 (1998)]. 1. T. I. Kamins, E. C. Carr, R. S. Williams, and S. J. Rosner, J. Appl. Phys. 81, 211 (1997). 8. N. V. Vostokov, Yu. N. Drozdov, Z. F. Krasil’nik, et al., Pis’ma Zh. Éksp. Teor. Fiz. 76 (6), 425 (2002) [JETP 2. O. P. Pchelyakov, Yu. B. Bolkhovityanov, A. V. Dvurech- Lett. 76, 365 (2002)]. enskiœ, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 34, 1281 (2000) [Semiconductors 34, 1229 (2000)]. 9. P. Sutter, E. Mateeva, J. S. Sullivan, and M. G. Lagally, 3. M. W. Dashiell, U. Denker, C. Muller, et al., Appl. Phys. Thin Solid Films 336, 262 (1998). Lett. 80, 1279 (2002). 10. A. Rastelli, E. Muller, and H. von Kanel, Appl. Phys. 4. A. V. Novikov, B. A. Andreev, N. V. Vostokov, et al., Lett. 80, 1438 (2002). Mater. Sci. Eng. B 89, 62 (2002). 5. U.-W. Mo, D. E. Savage, B. S. Swartzentruber, and M. G. Lagally, Phys. Rev. Lett. 65, 1020 (1990). Translated by G. Skrebtsov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 64Ð66. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 67Ð69. Original Russian Text Copyright © 2004 by Bolkhovityanov, Krivoshchapov, Nikiforov, Ol’shanetskiœ, Pchelyakov, Sokolov, Teys. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Synthesis of Ordered GeÐSi Heterostructures Containing Ultrasmall Germanium Nanoclusters Yu. B. Bolkhovityanov, S. Ts. Krivoshchapov, A. I. Nikiforov, B. Z. Ol’shanetskiœ, O. P. Pchelyakov, L. V. Sokolov, and S. A. Teys Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia e-mail: [email protected]

Abstract—Different techniques for the fabrication of structures containing ensembles of ultrasmall germanium nanoclusters distributed with a high density over the substrate surface are discussed. How to control the morphology and ordering of these ensembles is also discussed. © 2004 MAIK “Nauka/Interperiodica”.

With the advent of quantum nanostructures (espe- tems is still growing. To expand the use of Si-based cially of the structures containing quantum dots), the structures containing germanium nanoclusters, it is traditional, indirect-gap semiconductors Si and Ge are important to find ways to decrease the size of such nan- being considered as promising optical materials. This is oclusters and increase their surface density and degree the main reason behind the continuously increasing of ordering. interest in studying silicon- and germanium-based The present concepts on the early stage of self- quantum structures. In particular, the physical effects assembling and ordering of nanoclusters during Ge and that have been observed experimentally in these struc- Si heteroepitaxy have been analyzed in a number of tures in recent years are used to create an element basis reviews [4Ð8]. It has been shown that the formation of for microwave electronics in the gigahertz and terahertz nanoclusters at temperatures above 600°C is affected range, optical electronic devices, and quantum com- by interdiffusion [9]. puter engineering. Thus, the development of techniques for fabricating Si-based nanostructures containing ultr- The transition from layer-by-layer growth to nucle- asmall (<5 nm) germanium quantum dots is of great ation of three-dimensional (3D) islands has been stud- importance. ied in the Ge-on-Si heterosystem for a long time. At relatively low synthesis temperatures (300Ð500°C), the The ordering effect observed in arrays of quantum- interdiffusion between the deposit and substrate can be size islands in GeÐSi heterostructures makes it possible neglected [10, 11]. As was first shown in [4], there are to produce systems of defect-free quantum dots that are no misfit dislocations in such islands, even when the relatively small in size (10Ð100 nm) with a surface den- island thickness significantly exceeds the critical thick- sity of 1010Ð1011 cmÐ2. In this case, the atomic-like ness. It was precisely these publications that launched characteristics observed in the electronic and optical intensive studies into the formation mechanism of spectra of these objects become more pronounced. It is stressed islands and the peculiarities in their ordering: no wonder that these heterostructures were used to it was found how to produce arrays of defect-free 3D reveal single-electron effects in an array of islands for nanoobjects, which are of practical significance in the first time [1]. However, the majority of the subse- nanoelectronics. quent studies were devoted to the electronic properties Apart from the difference in the internal and surface of quantum dots in IIIÐV compounds. This was due to energies, lattice parameters, and elastic strains between a number of factors: (1) the impressive progress made epitaxial films and three-dimensional Ge islands on Si in the field of heteroepitaxy of III–V compounds; substrates, the main factor affecting the initial stage of (2) the possibility of producing type-I heterostructures heteroepitaxy is the film–substrate interface energy, as (in which the jumps in the conduction and valence well as the structure and composition of the Si-subbands are opposite in sign), which is significant for the strate surface, which determine the interface energy. In optical properties of systems; and (3) the small effec- particular, these factors determine the morphological tive masses of charge carriers, which makes it possible stability of the continuous pseudomorphic (wetting) Ge to observe size-quantization effects at relatively large layer, on which island self-assembling occurs at the island sizes. InAs–GaAs structures were the first III–V later stages of the growth (StranskiÐKrastanow mecha- compounds used to investigate the properties of quan- nism). These factors also affect the form, size, and spa- tum dots [2, 3]; presently, the interest in such nanosys- tial distribution of Ge nanoclusters in the first atomic

SYNTHESIS OF ORDERED GeÐSi HETEROSTRUCTURES 65 layers, whose coalescence results in the formation of a wetting layer. The formation of 3D islands involves an early stage of island nucleation followed by further development of the island nuclei. The key features of the island nucleation in the epitaxial heterosystem are determined by the energy balance between the deposit and substrate surfaces and by the balance between the layerÐ substrate interface energy and the internal volume energy of the islands. The free energy of a newly formed nucleus on the substrate surface can be written as a sum of three terms [12]: ∆ ∆µ γ (), G = ÐV ++sEi Vh/l . Here, the first term is the work required to produce a new nucleus of volume V, ∆µ is the thermodynamic driving force of crystallization (supersaturation), the 01020nm second term is the work required to form the extra surface area s, and γ is the surface energy of the nucleus Fig. 1. STM image of Ge nanoclusters on the Si (111) 7 × 7 (strictly speaking, this term should take into account the surface. difference between the nucleus surface energy and the substrateÐnucleus interface energy). The third term is In the case of homoepitaxy, when the stresses in the the additional energy associated with elastic strains of layer are minimal, 3D islands are not nucleated on the the nucleus. The first two terms in this expression are sufficiently clean surface of any semiconductor and a the classical version of the nucleation theory (see, e.g., [13]), whereas the last term appears only in the case of film grows either through the step motion (stepÐlayer stressed island films. When the lattice misfits are as growth) or through the nucleation and coalescence of large as those in the GeÐSi system, this additional 2D islands. Similar to homoepitaxy, strains are insig- energy depends not only on the volume of the nucleus nificant at the earliest stages of the heteroepitaxy; the but also on its shape (h/l is the ratio of the nucleus surface condition of the substrate is a more important height to the its lateral size). Thus, the third term in the factor in this case. For this reason, the morphology of above equation is of importance in the transition from the growth of the first monolayer on atomically clean the two-dimensional (2D) to 3D configuration. Accord- surfaces in the cases of homoepitaxy and heteroepitaxy ing to the calculations performed in [12], this term is a is the same. Thus, it can be concluded that the self- rapidly decreasing function of h/l. The more pro- assembling of ultrasmall nanoislands can be observed nounced the three-dimensional character of a stressed at the initial stage of the growth of the pseudomorphic nucleus, the more noticeable the effect of elastic relax- wetting Ge layer through the formation of 2D islands. ation (decrease in strains in the regions of the nucleus The shape and surface distribution of the islands can be that are most remote from the substrate) and the smaller controlled by changing the structural state of the Si- the additional contribution from the strains to the free layer surface, which was experimentally confirmed in energy of the nucleus. The surface energy of the “Ge [16Ð21]. The influence of 7 × 7 reconstruction of the Si layer (and the Ge island)–Si substrate” system also (111) surface on the formation of metal (In, Mn, Ag) depends on the Ge layer thickness and the germanium- [18] and Ge [17Ð20] nanoclusters less than 5 nm in size island shape [14]. In particular, a decrease in the thick- was demonstrated in [18, 19] (Fig. 1). It was shown that ness of the Ge layer results in a more pronounced metal and Ge nuclei arise primarily inside the half of dependence of the island shape on the interface energy. the 7 × 7 unit cell in the stacking-fault position. Such This statement was confirmed in [15, 16], where it was clusters are characterized by significant temperature experimentally shown that dense arrays of ultrasmall stability. Even after annealing at 350°C over 2 h, frag- quantum dots can be produced by depositing CaF2 lay- ments of nanoclusters remain on the Si surface between ers and oxygen monolayers. However, the ordering of relatively large Ge islands (Fig. 2). Ge quantum dots might be expected to be most pronounced in the case of heteroepitaxy on a clean single- It is likely that nanocluster ordering can be con- crystal Si surface. In spite of the extremely large num- trolled by using impurity superstructures, whose unit ber of experimental studies and detailed analytical cells can have different sizes and structure. In particu- reviews [4Ð8], no evidence has been reported that an lar, such superstructures can be formed on the Si sur- array of ordered nanoclusters can arise in the course of face by metal impurities (see, e.g., [22Ð24]). To date, formation of a pseudomorphic wetting layer. Let us these conjectures have not been confirmed experimen- consider several aspects of this problem. tally and stimulate further detailed studies of the mech-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

66 BOLKHOVITYANOV et al.

6. P. Moriarty, Rep. Prog. Phys. 64, 297 (2001). 7. T. I. Kamins, K. Nauka, and R. S. Williams, Appl. Phys. A 73, 1 (2001). 8. K. Brunner, Rep. Prog. Phys. 65, 27 (2002). 9. N. V. Vostokov, I. V. Dolgov, Yu. N. Drozdov, et al., J. Cryst. Growth 209, 302 (2000). 10. T. I. Kamins, G. Medeiros-Ribeiro, D. A. A. Ohlberg, and R. Stanley Williams, J. Appl. Phys. 85, 1159 (1999). 11. G. Capellini, M. De Seta, and F. Evangelisti, Appl. Phys. (a) (b) Lett. 78 (3), 303 (2001). 0 20 40 nm 0 20 40 nm 12. P. Müller and R. Kern, J. Cryst. Growth 193, 257 (1998). 13. A. A. Chernov, E. I. Givargizov, and Kh. S. Bagdasarov, Fig. 2. STM images of the Si (111) 7 × 7 surface with Ge Modern Crystallography, Ed. by B. K. Vaœnshteœn, nanoclusters and islands at a 0.4-bilayer coverage (a) before A. A. Chernov, and L. A. Shuvalov (Nauka, Moscow, and (b) after 2-h annealing at 350°C. 1980), Vol. 3. 14. F. Liu and M. G. Lagally, Phys. Rev. Lett. 76, 3156 anisms of semiconductor nanocluster ordering through (1996). the modiﬁcation of surface superstructures. 15. A. I. Yakimov, A. S. Derjabin, L. V. Sokolov, et al., Appl. Phys. Lett. 81 (3), 499 (2002). 16. A. I. Nikiforov, V. A. Cherepanov, and O. P. Pchelyakov, ACKNOWLEDGMENTS Mater. Sci. Eng. B 89 (1Ð3), 180 (2002). 17. U. Kohler, O. Jusuko, G. Pietch, et al., Surf. Sci. 321, This work was supported by the Russian Foundation 248 (1991). for Basic Research (project no. 03-02-16506-a) and the Ministry of Industry, Science, and Technology of the 18. S. A. Teys and B. Z. Olshanetsky, Phys. Low-Dimens. Semicond. Struct., Nos. 1Ð2, 37 (2002). Russian Federation (state contract no. 37.039.1.1.0041). 19. O. P. Pchelyakov, Yu. B. Bolkhovityanov, A. I. Nikiforov, et al., NATO Sci. Ser. 2: Math., Phys., Chem. 65, 371 (2001). REFERENCES 20. J. Li, J. Jia, X. Liang, et al., Phys. Rev. Lett. 88, 066101 (2002). 1. A. I. Yakimov, V. A. Markov, A. V. Dvurechenskii, and O. P. Pchelyakov, Philos. Mag. 65, 701 (1992). 21. L. Yan, H. Yang, H. Gao, et al., Surf. Sci. 498, 83 (2002). 22. O. Hellman, J. Appl. Phys. 76, 3818 (1994). 2. D. Leonard, M. Krishnamurthy, C. M. Reaves, et al., Appl. Phys. Lett. 63, 3203 (1993). 23. S. Parikh, M. Lee, and P. Bennett, Surf. Sci. 356, 53 (1996). 3. J.-M. Marzin, J.-M. Gerard, A. Izrael, and D. Barrier, Phys. Rev. Lett. 73, 716 (1994). 24. X. Lin, H. Mai, I. Chizhov, and R. Willis, J. Vac. Sci. Technol. B 14, 995 (1996). 4. D. J. Eaglesham and M. Cerullo, Phys. Rev. Lett. 64, 1943 (1990). 5. F. Liu and M. G. Lagally, Surf. Sci. 386, 169 (1997). Translated by A. Poushnov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 67Ð70. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 70Ð73. Original Russian Text Copyright © 2004 by Valakh, Dzhagan, Krasil’nik, Lytvyn, Lobanov, Mozdor, Novikov, Yukhymchuk, Yaremko.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Correlation between the Energy of SiGe Nanoislands and Their Shape and Size M. Ya. Valakh*, V. N. Dzhagan*, Z. F. Krasil’nik**, P. M. Lytvyn*, D. N. Lobanov**, E. V. Mozdor*, A. V. Novikov**, V. A. Yukhymchuk*, and A. M. Yaremko* * Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, 03028 Ukraine e-mail: [email protected] ** Institute of Microstructure Physics, Russian Academy of Sciences, Nizhni Novgorod, 603600 Russia

Abstract—The total energy of self-assembled SiGe nanoislands on a silicon substrate is investigated theoretically as a function of their geometric and physical parameters. It is demonstrated that the growth temperature and the silicon content in nanoislands affect the minimum of their energy. The results of numerical calculations for nanoislands are compared with experimental data obtained by atomic-force microscopy. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION 3. EXPERIMENTAL RESULTS Self-assembled germanium nanoislands grown Examination of the AFM images of the structures with nanoislands revealed that the size distribution of through molecular-beam epitaxy of germanium on sili- nanoislands can be either bimodal or unimodal depend- con or Si1 Ð xGex substrates have been intensively stud- ing on the growth temperature and the number of ied in recent years. The considerable interest expressed deposited germanium monolayers. This is explained by in these objects is associated with both the fundamental the fact that the nanoislands grown on the surface can aspects of problems in the physics of nanometer-sized have both pyramidal and domal shapes or only one of solid-state structures and possible practical applica- these shapes. The size and shape of the nanoislands tions [1]. depend on the growth temperature. An increase in the temperature of epitaxial deposition of germanium Despite the large number of papers devoted to the brings about a change in the chemical potential of the formation of nanoislands, the mechanisms responsible structure and an increase in the coefficient of diffusion for the formation of nanoislands in the form of pyra- of silicon atoms from the silicon substrate to the mids or domes and for the transition from one form to nanoislands. Analysis of the AFM images demon- another are not clearly understood. The elucidation of strated that, during the growth, the pyramidal nanois- these mechanisms is the main subject of our investi- lands retain their shape due to a proportional increase gation. in their lateral sizes and height. After the critical volume is reached, the pyramids transform into dome- shaped nanoislands owing to the formation of new lat- 2. SAMPLES AND EXPERIMENTAL eral facets whose angles with the substrate are greater TECHNIQUE than those of the pyramids. The changes in the shape of the nanoislands are caused by a more efficient relax- The structures studied in this work were prepared by ation of stresses in nanoislands with a larger ratio of the molecular-beam epitaxy on a Si(001) substrate with a height to the lateral size [2]. 200-nm-thick buffer silicon layer preliminarily grown on it. Two series of samples were used in our experiments. For samples of the first series, the thickness of 4. THEORETICAL ANALYSIS AND DISCUSSION germanium layers was varied from 5.5 to 11 monolayers (ML) and the growth temperature was constant and 4.1. Energy of the Strained Structure equal to 700°C. For samples of the second series, the An analytic expression describing the energy of a thickness of germanium layers was constant and equal dislocation-free germanium island was derived by Ter- to 9 ML but the epitaxial growth was carried out at dif- soff et al. [3, 4]. This expression makes it possible to ferent temperatures (600, 700, 750°C). The size and analyze the changes in the shape of the island. When shape of the nanoislands were controlled using a Nano- deriving this expression, those authors made the fol- scope III-a atomic-force microscope (AFM). lowing assumptions: (a) the island in the form of a trun-

68 VALAKH et al. γ γ cated pyramid of height h has a rectangular base of does not depend on the physical parameters c, s, e, width s and length t, and (b) the base forms an angle θ etc., which is surprising. Moreover, as was shown by with any lateral facet of the island. Zhang and Bower [5], the shape of the nanoislands The total energy of the island can be represented in should depend not only on the energy but also on the the form kinetic processes. In this connection, we once again consider the problem formulated in [3, 4] in order to EE= s + Er, (1) analyze relationships (1)Ð(3) taking into account all γ γ θ quantities, namely, s, t, h, s, e, and . By varying these where Es is the total energy of the surface and the interface and E is the change in the elastic energy due to parameters, we can judge the presence or absence of the r global minimum of the energy E and elucidate how the relaxation. The expression for Es has the form growth temperature, the deposition rate, and the num- ()γ γ γ () ber of germanium monolayers affect the parameters of Es = st i + t Ð s + 2 st+ (2) the nanoislands. × []γ θ θγ()γ γ h e cosec Ð hcot t + s Ð i /2 , Expressions (1)Ð(3) can be conveniently written in γ γ γ γ relative units: where s, e, t, and i are the surface energies (per unit area) of the substrate, the facets and the top of the γ γ γ γ s˜ ==s/h, ˜t t/h, ˜ e =/ch, ˜ s =/ch. (4) island, and the islandÐsubstrate interface, respectively. e s In the case where the growth of nanoislands occurs In this case, the expression for the total energy takes the through the StranskiÐKrastanov mechanism, expres- form sion (2) can be simpliﬁed because γ = γ and γ = 0 [3]. t s i  3 ()γ()θ γ θ The relaxation energy in a quasi-two-dimensional E = 2ch  s˜ + ˜t ˜ e cosec Ð ˜ s cot - approximation (s ӷ h, t ӷ h) has the following form:  (5) 2[ ()3/2 θ Er = Ð2ch steln /hcot ˜ ˜  (3) ˜ t ˜ s 3/2 Ð sln------+ t ln------, + tseln()/hcotθ ]. αθcot αθcot 

2 3 Here, c = σ (1 Ð ν)/2πµ, σ stands for the components Ð--- b b 2 of the stress tensor for bulk germanium; and ν and µ are where α = e . In this model, h is a constant and the the Poisson ratio and the shear modulus of the silicon product ch3 has the dimension of energy (all the other substrate, respectively. quantities in braces are expressed in relative units). This It follows from relationships (1)Ð(3) that the total function is too composite to be treated analytically. energy of an island cannot be expressed as a function of Therefore, we analyzed this function numerically. The the volume, because it is a composite function of the results obtained are presented in Figs. 1Ð3. This simu- lateral sizes (s, t), height (h), angle (θ), and volume (c) lation demonstrated that the dependence E(θ) can have and surface parameters (γ , γ ) of the island. According a minimum at angles in the range 0 < θ < π/2, provided s e γ γ to the model proposed by Tersoff and Tromp [3], the the values of ˜ s and ˜ e are close or equal to each other height h increases slowly as compared to the parame- (Fig. 1). It should be noted that, in this case, we ana- ters s and t; hence, it can be considered to be constant. lyzed the dependence E(θ) only mathematically by In [3, 4], the energy E of a nanoisland was analyzed varying different parameters and not imposing physical in two cases. limitations. All the physical conclusions should be (A) The total volume was not fixed, and the specific related to the minimum of the energy E. The numerical energy E/V was minimized instead of the energy E to analysis demonstrates (Fig. 1) that the minimum of the energy E appears only when the values of γ˜ and γ˜ are give s = t = a0. However, the existence of a minimum of s e γ the energy E at these values of s and t does not follow not very small (in our case, when the values of ˜ s and from the mere fact that the specific energy E/V has a γ˜ are greater than or equal to 5). On the other hand, minimum at the same parameters. Furthermore, the e γ γ minimum of the energy E can exist in quite a different under the condition ˜ s < ˜ e (Fig. 1, curve 7), the min- ≠ θ π region (s, t a0). Therefore, the physical conclusions imum energy Emin corresponds to the angle = /2 and drawn from the above consideration call for detailed the nanoisland should grow in the form of a prism. Note θ analysis. Evidently, this reasoning was obvious to that the minimum energy Emin and the relevant angle Tersoff and LeGoues [4], and they considered another (Fig. 2) depend on the ratio between γ˜ and γ˜ (at con- case (B). s e ˜ ˜ (B) The energy E was minimized in [4] at a fixed stant values of s and t ), which disagrees with the volume of the nanoisland. It was found that the mini- results obtained in [4]. From analyzing the results pre- mum of the energy E corresponds to the parameters s = sented in Fig. 2, we can conclude that there do not exist t = hcotθ, depends only on the geometric sizes, and such values of s˜ and ˜t for which the energy E has a glo-

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 CORRELATION BETWEEN THE ENERGY OF SiGe NANOISLANDS 69

800 0 7 1 600 2 6 –500 3 400

200 –1000 5 4 0 4 –1500 5 –200 Energy, arb. units

Energy, arb. units 3 –400 –2000 6 2 –600 1 –2500 –800 0 0.5 1.0 1.5 0 0.5 1.0 1.5 θ θ, rad , rad Fig. 2. Dependences of the energy of a nanoisland on the Fig. 1. Dependences of the energy of a nanoisland on the angle θ at constant parameters γ˜ = γ˜ = 6 and different θ ˜ γ˜ s e angle at constant parameters s˜ = t = 5 and s = 5 and the parameters s˜ and ˜t (s˜ = ˜t ): (1) 10, (2) 50, (3) 100, (4) 150, γ˜ parameter e ranging from (1) 4.6 to (7) 5.8. (5) 200, and (6) 250. bal minimum: the larger the values of s˜ and ˜t , the thermal expansion coefficients of SiGe nanoislands and lower the energy of the system. Therefore, theoreti- the silicon substrate. According to the thermodynamics cally, the values of s and t tend to increase indefinitely. of a strained system [6], the mechanical stress can be σ σ α It can be seen from Fig. 1 that, at given constant represented in the form b = b0 + K T(T Ð T0), where σ ˜ ˜ γ˜ γ˜ b0 is the stress at a temperature T0, K is the bulk mod- parameters s , t , and s , the change in e leads only to a α θ ulus, T is the thermal expansion coefficient, and T Ð T0 shift of the curves E( ) but does not result in their inter- is the difference between the temperatures. The section. However, these curves can intersect other curves mechanical stresses increase in proportion to the differ- (the figure for this is not presented) corresponding to dif- ence α Ð α with an increase in the temperature. In ˜ γ˜ Si Ge ferent values of s˜ and t and to equal values of e . the temperature range where this difference is constant, the mechanical stress takes the form

4.2. The Influence of the Growth Temperature σ σ β T ()α and Silicon Content in Nanoislands b = b0 1 +1T -----Ð 1 Ð c x , T 0 on the Total Energy E of Nanoislands (6) ∆α All the above reasoning concerns only nanoislands β K T T 0 T = ------σ . of pure germanium. The experimental results obtained b0 by many authors, particularly by Krasilnik et al. [2], It should be noted that, in a certain temperature range, demonstrate that the growth of germanium nanoislands α on a silicon substrate is accompanied by the diffusion the thermal expansion coefficient T and the silicon of silicon atoms. The content of silicon in nanoislands content x oppositely affect the mechanical stresses in σ increases with an increase in the growth temperature, the nanoisland and the resultant stress b depends on which is confirmed by Raman spectroscopy [2]. As the which of these factors predominates. content of silicon in nanoislands increases, the lattice Figure 3 shows the dependences E(θ) for three sets mismatch between the nanoislands and the substrate of parameters s˜ and ˜t at x = 0 and 0.5. It can be seen becomes less pronounced and, consequently, the from this figure that, in the case where silicon is absent stresses in the nanoislands decrease. In a linear approx- σ in nanoislands (x = 0, curves 1), all the dependences imation, we can write the following relationship: b = exhibit a minimum and E < 0. As the content of sili- σ (1 Ð α x), where α is an arbitrary factor in the range min b0 c c con in the nanoislands increases to 0.5, the values of γ˜ 0 < α < 1. s c γ˜ There exists one more factor affecting the mechani- and e change in accordance with relationships (4) and σ 2 cal stresses due to the difference between the linear the dependence c ~ ( b) ; this leads to an upward shift

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 70 VALAKH et al.

˜t , s˜ = t, s/h are unstable. This means that, at constant 150 parameters t and s, the nanoislands with the largest heights h will dissociate ﬁrst.

100 5. CONCLUSIONS Thus, the detailed analysis of the growth of strained SiGe nanoislands demonstrated that their size depends on the growth temperature, silicon content in the

50 { nanoislands, and number of deposited germanium 3 monolayers. The results of numerical treatment

Energy, arb. units allowed us to conclude that the decrease in the elastic { 2 energy of the nanoislands leads to an increase in their

0 lateral size as compared to the height. The increase in { the growth temperature affects the ratio between the 1 surface and volume characteristics of the nanoislands in a complicated manner. For given values of tempera- –50 0 0.5 1.0 1.5 ture, silicon content in the nanoislands, and growth θ, rad time, there exists a limiting ratio of the height to the lateral size which determines the shape of the nanoislands. Fig. 3. Dependences of the energy of a nanoisland on the angle θ for three sets of parameters x and β (x is the silicon content in the nanoisland, and β is the thermal expansion coefficient): (1) x = 0, β = 0; (2) x = 0.5, β = 0.3; and (3) x = ACKNOWLEDGMENTS 0.5, β = 0. In each set, the solid, dashed, and dotted lines This work was supported by the UkrainianÐRussian correspond to parameters s˜ = ˜t = 10, s˜ = ˜t = 12, and s˜ = program “Nanophysics” and the International Associa- ˜t = 15, respectively. tion of Assistance for the promotion of cooperation with scientists from the New Independent States of the former Soviet Union, project no. INTAS 01 0444. of the dependences E(θ), two of which exhibit a minimum energy Emin > 0 (Fig. 3, curves 3). From the physical standpoint, this means that the nucleated islands REFERENCES will dissociate at these parameters. Taking into account 1. K. Bruner, Rep. Prog. Phys. 65, 27 (2002). the thermal expansion coefficients (β ≠ 0), we can 2. Z. F. Krasilnik, P. M. Lytvyn, D. N. Lobanov, et al., Nan- obtain the dependences represented by the series of otechnology 13, 81 (2002). curves 2. In this case, the total energy E changes more 3. J. Tersoff and R. M. Tromp, Phys. Rev. Lett. 70 (18), slowly than that for β = 0 and all nanoislands are 2782 (1993). retained, because, for all curves 2, we have Emin < 0, 4. J. Tersoff and F. K. LeGoues, Phys. Rev. Lett. 72 (22), unlike the two upper curves 3. This result demonstrates 3570 (1994). that the effects associated with variations in the silicon 5. Y. W. Zhang and A. F. Bower, Appl. Phys. Lett. 78 (18), content x in the nanoislands and those caused by 2706 (2001). changes in the thermal expansion coefficients β can 6. L. D. Landau and E. M. Lifshitz, Course of Theoretical partially compensate for each other; consequently, the Physics, Vol. 7: Theory of Elasticity, 4th ed. (Pergamon, New York, 1986; Nauka, Moscow, 1987). relative sizes (h/t, s) of the nanoislands change insignificantly as the temperature increases. It can also be seen from Fig. 3 that the nanoislands with small parameters Translated by O. Moskalev

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 71Ð73. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 74Ð76. Original Russian Text Copyright © 2004 by Burbaev, Kurbatov, Pogosov, Rzaev, Sibel’din, Tsvetkov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Photoluminescence of Si/Ge Nanostructures Grown by Molecular-Beam Epitaxy at Low Temperatures T. M. Burbaev, V. A. Kurbatov, A. O. Pogosov, M. M. Rzaev, N. N. Sibel’din, and V. A. Tsvetkov Lebedev Physical Institute, Russian Academy of Sciences, Leninskiœ pr. 53, Moscow, 119991 Russia e-mail: [email protected]

Abstract—Multilayer Si/Ge nanostructures grown by molecular-beam epitaxy at low temperatures (250Ð 300°C) of germanium deposition are studied using photoluminescence and atomic-force microscopy (AFM). It is assumed that, upon low-temperature epitaxy, the wetting layer is formed through the intergrowth of two- dimensional (2D) and three-dimensional (3D) nanoislands. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION nological thickness of 2Ð12 ML. For AFM observa- It is known that high-temperature (500Ð700°C) epi- tions, the upper germanium layer of samples was not taxy of germanium on silicon proceeds according to the covered with silicon. The growth rate of silicon and StranskiÐKrastanov mechanism. A continuous strained germanium layers was equal to 0.005 nm/s. (wetting) layer of germanium is formed when the thick- During the growth of nanostructures, we observed ness of the germanium layer becomes equal to approx- reflection high-energy electron diffraction (RHEED) imately two monolayers (ML). In the silicon matrix, patterns. At 250°C, the initial reconstruction of the sil- this layer manifests itself as a quantum well for holes. icon surface was retained in the course of the growth of In the case when the critical thickness exceeds 4 ML, all nanostructures (the thickest germanium layer was there arise three-dimensional nanoislands, namely, equal to 10 ML). The main reflections were smeared quantum dots, on the strained wetting layer [1Ð4]. It is and broadened only slightly. At 300°C, three-dimen- also known that, at an epitaxy temperature of 360°C sional growth was observed only in the case when the and below, the formation of nanoislands is suppressed technological thickness of the germanium layer was because of the low rate of diffusion of adatoms [4]. At 12 ML. Examination of the growth of nanostructures at first glance, these data disagree with the results these temperatures allowed us to conclude that no obtained in previous investigations into the properties three-dimensional growth of nanoislands through the of islands grown by epitaxy in the temperature range StranskiÐKrastanov mechanism occurs at 250°C; how- 200Ð300°C [5Ð7]. ever, at 300°C, three-dimensional islands are formed by In this work, the structural and optical properties of this mechanism when the thickness of the germanium Si/Ge nanostructures grown through molecular-beam layer reaches 12 ML. epitaxy at low temperatures (250Ð300°C) were investi- The surface morphology was analyzed using an gated using photoluminescence and atomic-force AFM SOLVER P47 atomic-force microscope. The microscopy (AFM). photoluminescence spectra were measured at a temperature of 2 K. A semiconductor laser (λ = 0.66 µm) was used as an excitation source (hν = 1.87 eV). The highest 2. SAMPLES radiation power was 70 mW, and the radiation power AND EXPERIMENTAL TECHNIQUE density at the sample usually amounted to 4 W/cm2. The nanostructures used in our experiments were The radiation from the samples was measured using a grown using a Riber SIVA 45 apparatus at the Institute nitrogen-cooled germanium pÐiÐn photodiode. of Semiconductor Physics, Linz University, Austria. It should be noted that a change in the germanium layer 3. RESULTS AND DISCUSSION thickness by only 1 ML brings about significant variations in the morphology and optical properties of the Figure 1 shows the AFM images of the surfaces of nanostructures. For this reason, all the structures under the structures grown at a temperature of 300°C. For a investigation should be grown using the same appara- germanium layer thicker than 2 ML, the surface of the tus. All the structures grown consisted of four or five structure contains large-sized flat islands (500 × 500 × layers. Each layer was composed of a silicon layer 0.5 nm3), which do not cover extended surface regions. 25.5 nm thick and a germanium layer with a mean tech- For a layer thickness of 3 ML, the lateral sizes of

72 BURBAEV et al.

(a) QW–NP BE–TO QW–TO BE–TO (a) complex QD FE–TO 4 600 33

2 600 WL

nm 300 PL intensity, arb. units 1 1 QW–NP 300

nm ~ ~ 700 800 900 1000 1080 1100 0 Energy, meV BE–TO (b) (b) QW–TO 2000 QW–NP 6

nm 1000 4 QD 2000 PL intensity, arb. units 1 2 3 1000 nm 700 800 900 1000 1100 Energy, meV 0

Fig. 2. Photoluminescence spectra of the Si/Ge nanostruc- (c) tures grown at temperatures of (a) 300 and (b) 250°C. For clarity, the spectra are shifted along the ordinate axis. Mean thickness of germanium layers: (a) (1) 5, (2) 3.5, (3) 3, and 2000 (4) 2.5 and (b) (1) 7, (2) 5, (3) 3.5, (4) 3, (5) 2.5, and (6) 2 ML. Designations: QWÐTO and QWÐNP are the phonon (silicon) and zero-phonon lines of the quantum- well emission, respectively; QD is the line of the quantum- 1000 dot emission; BEÐTO complex and BEÐTO are the phonon nm 2000 lines of emission of bound-exciton complexes and bound excitons in silicon, respectively; FEÐTO is the line of emis- 1000 sion of free excitons in silicon; and WL is the wetting layer. nm 0 Fig. 1. AFM images of the surfaces of the structures grown The above inference is conﬁrmed by the results of at a temperature of 300°C. Mean thickness of germanium analyzing the photoluminescence spectra shown in layers in the structures: (a) 3, (b) 5, and (c) 12 ML. Fig. 2. Figure 2a illustrates the evolution of the emission spectra of 2D and 3D nanoislands with an increase ≈ in the thickness of the germanium layer. As the layer islands decrease to 30 nm and they cover extended thickness increases from 2 to 3 ML, the intensity of surface regions (Fig. 1a). However, when the layer quantum-well emission decreases, whereas the inten- thickness increases to 5 ML, the surface becomes sity of quantum-dot emission increases. However, with smooth and the island relief disappears (Fig. 1b). In the a further increase in the layer thickness to 5 ML, the case when the mean thickness of the germanium layer emission of 2D and 3D nanoislands almost ceases and reaches 10Ð12 ML, the islands with a lateral size ≥ a line appears at an energy of 1080 meV. This line is 50 nm arise again (Fig. 1c). attributed to the wetting layer. For a germanium layer We assume that, during the growth of nanostruc- thicker than 7 ML, the emission of the wetting layer tures at 300°C, a wetting layer with a thickness of 3Ð also vanishes and only the emission of the silicon sub- 5 ML is formed through the coalescence of two-dimen- strate manifests itself in the spectra. sional (2D) and three-dimensional (3D) nanoislands. It should be noted that the dependence of the energy For a layer thickness of 10Ð12 ML, the quantum dots location of the zero-phonon line in the photolumines- are formed on the wetting layer according to the Stran- cence spectrum of 2D nanoislands on the mean thick- skiÐKrastanov mechanism. ness of germanium layers lies substantially below the

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

PHOTOLUMINESCENCE OF Si/Ge NANOSTRUCTURES GROWN 73 theoretical curve for the strained germanium layer on ACKNOWLEDGMENTS the silicon substrate [8] and corresponds to a partially We would like to thank Professor F. Schefﬂer for relaxed layer. The photoluminescence line of the wet- providing an opportunity to perform our investigations ting layer is located at an energy of 1080 meV, which is at his laboratory. close to the energy predicted from the theoretical curve This work was supported by the Russian Foundation [8], and corresponds to the strained germanium layer. for Basic Research (project no. 03-02-17191), the An analogous conclusion regarding partial relaxation “Low-Dimensional Quantum Structures” program of of the germanium layer, which precedes the formation the Presidium of the Russian Academy of Sciences of the wetting layer, was drawn by us from analyzing (project no. 7.12), and the State Program of Support for the Raman spectra of the structures grown using a Leading Scientiﬁc Schools of the Russian Federation. KATUN’-type apparatus [9]. It should be noted that the quantum dots formed on a similar wetting layer REFERENCES through the StranskiÐKrastanov mechanism exhibit 1. O. P. Pchelyakov, Yu. B. Bolkhovitinov, A. V. Dvurech- weak photoluminescence. enskiœ, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 34 The evolution of the photoluminescence spectra of (11), 1281 (2000) [Semiconductors 34, 1229 (2000)]. 2D and 3D nanoislands with an increase in the thick- 2. G. Abstreiter, P. Schittenhelm, C. Engel, et al., Semi- cond. Sci. Technol. 11, 1521 (1996). ness of the germanium layer for the nanostructures ° 3. P. Schittenhelm, C. Engel, F. Findeis, et al., J. Vac. Sci. grown at a temperature of 250 C is illustrated in Technol. B 16 (3), 1575 (1998). Fig. 2b. In this case, no continuous wetting layer is 4. O. G. Schmidt, C. Lange, and K. Eberl, Appl. Phys. Lett. formed at any thickness of the germanium layer. An 75, 1905 (1999). increase in the layer thickness in a narrow range (5Ð 5. A. B. Talochkin, A. V. Efanov, V. A. Markov, and 6 ML) leads to a considerable narrowing of the photo- A. I. Nikiforov, Izv. Ross. Akad. Nauk, Ser. Fiz. 63 (2), luminescence line of 3D nanoislands and an abrupt 290 (1999). increase in its intensity. 6. V. A. Markov, H. H. Cheng, Chih-ta Chia, et al., Thin Solid Films 369, 79 (2000). 7. T. M. Burbaev, T. N. Zavaritskaya, V. A. Kurbatov, et al., 4. CONCLUSIONS Fiz. Tekh. Poluprovodn. (St. Petersburg) 35 (8), 979 (2001) [Semiconductors 35, 941 (2001)]. Thus, the results obtained in this study demon- 8. J. Brunner, J. F. Nutzel, M. Gail, et al., J. Vac. Sci. Tech- strated that a decrease in the temperature of molecular- nol. B 11, 1097 (1993). beam epitaxy to 250Ð300°C leads to a radical change in 9. T. M. Burbaev, V. A. Kurbatov, T. N. Zavaritskaya, et al., the mechanism of growth of germanium on silicon. At Izv. Ross. Akad. Nauk, Ser. Fiz. 67 (2), 163 (2003). the initial stage of the growth, 2D and 3D nanoislands arise with no formation of a continuous wetting layer. Translated by N. Korovin

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 74Ð76. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 77Ð79. Original Russian Text Copyright © 2004 by Shegaœ, Markov, Nikiforov. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Stepwise Dependence of the Photoconductivity of Si/Ge Structures with Quantum Dots on the Interband Illumination Intensity O. A. Shegaœ, V. A. Markov, and A. I. Nikiforov Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia e-mail: [email protected]

Abstract—It was found that a stepwise increase in the interband light intensity causes an increase in the low- temperature lateral photoconductivity of a Si/Ge structure containing six layers of germanium quantum dots in a silicon host. As was previously observed in structures with a single layer of quantum dots, strengthening of the driving ﬁeld results in the step positions shifting to lower light intensities. This effect was also found to take place under a dark driving ﬁeld. The results are discussed in terms of the percolation theory of nonequilibrium electrons localized in the states between quantum dots. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION lightÐemitting diode placed near the sample with an illuminated area of 1.5 × 0.2 mm. The signals propor- The study of the lateral photoconductivity (PC) tional to the sample conductivity and to the illumina- mechanisms in Si/Ge/Si structures containing self- tion intensity of the sample were recorded using a com- assembling germanium quantum dots (QDs) is of inter- puter. est because of the application potential of these structures in optoelectronics [1]. Previously, we reported on the detection of a stepwise increase in the lateral PC of 3. RESULTS AND DISCUSSION structures with a single QD layer caused by an increase in the interband illumination intensity [2, 3]. The Figure 1 shows the light-intensity dependences of observed effect was explained in terms of the theory of the lateral PC at various values of the driving field for a percolation [4] of nonequilibrium carriers over local- structure with six QD layers and NGe = 8 MLs and the ized states arising in the silicon matrix between QDs dependence of the step position on the driving field due to spatial stress relaxation in the vicinity of QDs (dots indicate experimental data, the curve is a result of [5]. In this paper, we report on the detection of a step- exponential fitting). Figure 2 shows analogous depen- wise increase in the PC signal under interband illumi- dences for a structure with NGe = 10 MLs. As in the pre- nation in structures with six germanium QD layers and vious study with a single QD layer [2, 3], a stepwise on the influence of a dark driving field on the step posi- increase in the PC signal is observed. The step positions tion. are shifted to lower light intensities with increasing driving field. As in the structure with a single QD layer, the dependence of this shift for the structure with N = 2. EXPERIMENTAL GS 8 MLs is exponential with a similar characteristic volt- ≈ Strained Si/Ge/Si structures were grown (using age value U0 2 V [2, 3]; for the structure with NGe = molecular-beam epitaxy) through the StranskiÐKrast- 10 MLs, this dependence is linear (Fig. 2). anow mechanism on Si(001) substrates and contained six QD layers with a nominal Ge thickness of N = 8 Figure 3 shows the influence of the dark driving Ge field on the PC step position in both QD structures. Ini- and 10 monolayers (MLs). The QD layers were sepa- tially, the dependence of the lateral PC on the interband rated by silicon layers 25 nm thick. The layers contain- light intensity was measured at a certain fixed value of ing QDs were grown on a buffer silicon layer ~100 nm the driving field. Then, a voltage of 100 V was applied thick and were coated by a cap Si layer ~20 nm thick. to the structure for a few seconds in the dark and the A decrease in the Ge layer growth temperature to T = g dependence of the PC was measured again at the initial ° ≈ 11 Ð2 250 C resulted in a high QD density (NQD 10 cm ) value of the driving field. We can see that the step is and small QD sizes (the lateral size was ~10 nm). shifted to lower light intensities after applying the volt- The PC was measured at T = 4.2 K. The light inten- age in the dark for both structures. The shift for the sity was swept by increasing the current through a red structure with NGe = 10 MLs exceeds that for the struc-

STEPWISE DEPENDENCE OF THE PHOTOCONDUCTIVITY 75

5 (a) 1800 (a)

–1 53 V NGe = 8 MLs 57 V 55 V Q 1600 6 layers 10 MLs × 6 layers –5 –5 4 52 V = 4.2 K 12 V 1400 T = 4.2 K T 51 V 17 V 13 V 1200 15 V 3 11 V 50 V 19 V 1000 800 2 600 1 400 Photoconductivity, 10

Photoconductivity, arb. units 200

0 5 10 15 20 024 6 8 10121416182022 Light intensity, arb. units Light intensity, arb. units 20 22 (b) (b) 18 20 18 16 16 14 14 12 12 10 10 Step position, arb. units Step position, arb. units 8 8 6 6 12 14 16 18 20 50 51 52 53 54 55 56 Lateral voltage, V Lateral voltage, V

Fig. 1. (a) Dependence of the lateral photoconductivity of a Fig. 2. The same as in Fig. 1 but for a nominal layer thick- structure with six QD layers (nominal thickness of each ness of 10 MLs. layer is 8 MLs) on the interband light intensity at various driving fields and (b) the dependence of the PC step position on the lateral field. QDs form exciton states, whose concentration is controlled by the interband light intensity and which do not ture with N = 8 MLs by approximately four times. It affect the structure conductivity. Strengthening of the Ge driving field results in splitting of the excitons into car- was indicated that the shift depends linearly on the dark riers localized in the same place. When the quasi-Fermi field. level of electrons that are in localized states between We analyzed the results of the study in terms of the QDs reaches the percolation threshold, a stepwise model of nonequilibrium carrier percolation over local- increase in the PC signal is observed. The higher the ized states between QDs suggested by us previously. lateral field, the larger the number of dissociated exci- These states arise due to spatial stress relaxation in the tons and the lower the light intensity at which the step vicinity of QDs [5]. The states are in the QD plane, with arises. The values of the lateral field at which a PC step each of these states being at the same distance from at arises are much higher for the structure with NGe = least three nearest QDs. Fluctuations in the distance 10 MLs than those for the structure with NGe = 8 MLs. between QDs and in their lateral size cause the localiza- This fact is explained by the larger energy band relief tion potential to fluctuate. amplitude caused by increased stresses in QDs in the Interband illumination causes localization of non- structures with larger QDs. equilibrium electrons in the states described above. At Apart from lateral relaxation of stresses around low interband light intensities, the concentration of QDs, transverse relaxation of stresses in the structure nonequilibrium carriers is lower than that of QDs and growth direction also takes place. Since the depen- holes are mostly localized in QD states. At high inten- dences of the PC on the interband light intensity for the sities, holes are localized between QDs. If the QD Cou- structure with NGe = 8 MLs almost do not differ from lomb potential that trapped a hole is higher than the those for the structures with a single QD layer, trans- repulsing potential due to the inhomogeneous stresses verse relaxation of stresses in the regions between in the vicinity of the QD, an electron forms a bound neighboring QD layers in the former structure is com- state on the QD [5]. Carriers localized in states between plete. For the structure with large lateral sizes of QDs

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

76 SHEGAŒ et al.

2000 4. CONCLUSIONS T = 4.2 K 1800 Thus, a stepwise increase has been detected in the 1600 dependence of the lateral photoconductivity of Si/Ge U = 52 V 1400 b structures with several QD layers on the interband light After darkness 1200 intensity. Strengthening of the driving field causes a voltage 100 V shift of the step position to lower light intensities. It has 1000 U = 14 V been found that the dark driving field affects the step 800 position, whose shift depends essentially on the QD lat- 600 a eral sizes. The results were interpreted in terms of the 400 theory of percolation over localized states arising due to spatial stress relaxation in the vicinity of quantum Photoconductivity, arb. units 200 dots. 0 5 10 15 20 Light intensity, arb. units ACKNOWLEDGMENTS Fig. 3. Influence of the dark voltage (100 V) on the inter- This study was supported by the Russian Founda- band light intensity dependence of the lateral photoconduc- tion for Basic Research, projects no. 03-02-16466 and tivity for structures containing six QD layers with a Ge layer 03-02-16468. thickness of (a) 8 MLs and (b) 10 MLs (for convenience, the curves are shifted upward). REFERENCES (NGe = 10 MLs) and identical distances between neigh- 1. O. P. Pchelyakov, Yu. B. Bolkhovityanov, A. V. Dvurech- boring QD layers, mutual strengthening of the strain enskiœ, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 34 fields takes place, which increases the band relief (11), 1281 (2000) [Semiconductors 34, 1229 (2000)]. amplitude. 2. O. A. Shegai, V. A. Markov, A. I. Nikiforov, et al., Phys. We are of the opinion that the PC step position shift Low-Dimens. Semicond. Struct. 1Ð2, 261 (2002). in the QD structures under a dark voltage is caused by 3. O. A. Shegaœ, K. S. Zhuravlev, V. A. Markov, et al., Izv. carrier injection from the contacts into the structure. Ross. Akad. Nauk, Ser. Fiz. 67 (2), 192 (2003). After the dark voltage is switched off, a certain fraction 4. B. I. Shklovskiœ and A. L. Éfros, Electronic Properties of of electrons can be in the localized states between QDs Doped Semiconductors (Nauka, Moscow, 1979; Springer, for a rather long time due to the band relief. In the struc- New York, 1984). ture with a high band relief potential (N = 10 MLs), Ge 5. O. A. Shegaœ, K. S. Zhuravlev, V. A. Markov, et al., Fiz. the number of electrons localized between QDs is Tekh. Poluprovodn. (St. Petersburg) 34 (11), 1363 larger than that in the structure with NGe = 8 MLs, (2000) [Semiconductors 34, 1311 (2000)]. which results in the percolation threshold being reached at significantly lower interband light intensities. Translated by A. Kazantsev

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 77Ð79. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 80Ð82. Original Russian Text Copyright © 2004 by Nikiforov, Ul’yanov, Pchelyakov, Teys, Gutakovskiœ. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Growth and Structure of Ge Nanoislands on an Atomically Clean Silicon Oxide Surface A. I. Nikiforov, V. V. Ul’yanov, O. P. Pchelyakov, S. A. Teys, and A. K. Gutakovskiœ Institite of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia e-mail: [email protected]

Abstract—Experimental data on the formation of self-organized Ge islands on an atomically clean oxidized Si(100) surface are presented. On the oxidized silicon surface, the VolmerÐWeber growth mechanism is operative rather than the StranskiÐKrastanow mechanism, which operates in the case of Ge growth on a clean silicon surface. The Ge growth is accompanied by a significant change (as large as 7%) in the surface unit cell size of the Ge lattice with respect to that for silicon. For Ge films up to five monolayers thick, the nanoisland dimensions at the bottom are smaller than 10 nm and the island density is higher than 2 × 1012 cmÐ2. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION grow on an oxidized Si(111) surface, their lateral dimensions are less than 10 nm and their density is The study of the self-organization of nanometer- higher than 1012 cmÐ2. In [5], it was suggested that in sized islands is of interest in several areas of solid-state this case silicon oxide is locally deoxidized by germa- physics. For surface physics and the physics of con- nium (through the disproportionation reaction), which densed matter, the study of the mechanisms of nanois accompanied by desorption of germanium monox- structure growth and of concomitant atomic processes ide. At such sites, germanium nanoislands jointed proceeding on the surface is of interest. Nanoislands coherently with the silicon nucleate. However, there are have also been a subject of considerable interest in no data on island deformation and its relaxation in ger- semiconductor physics, because they can be employed maniumÐsilicon oxide heterojunctions. as quantum-confinement systems. An example is the heterosystem of germanium grown on the Si surface, in The objective of this work is to determine the mech- which Ge islands can be treated as quantum dots. On anism of a Ge island film growing on an atomically the Si(100) surface, dislocation-free germanium clean oxidized Si surface and to produce an array of islands 10Ð100 nm in size were observed to appear after ultrasmall Ge nanoislands of high density. a continuous Ge film was formed [1]. Such islands can be made sufficiently small in size for the quantum-confinement effects to manifest themselves at temperatures 2. EXPERIMENT up to room temperature [2]. Island films were produced in a Katun’-S MBE The minimal size of Ge islands that form during film chamber. Silicon was evaporated using an electron- growth on a clean silicon surface is 15 nm. The size of beam evaporator (EBE). A germanium flux was formed Ge islands can be made smaller and their density higher either by the EBE or by an effusion cell with a boron by growing a germanium film on an atomically clean nitride crucible. Dopants (Sb, B) were evaporated from oxidized surface prepared directly in a molecular-beam effusion cells. Analysis was performed using a quadru- epitaxy (MBE) setup. The possibility of producing an pole mass spectrometer, a quartz crystal monitor, and a oxide layer on a silicon surface under conditions of an reflection high-energy electron (20 keV) diffractome- ultrahigh-vacuum has been known for a fairly long ter. Diffraction patterns were recorded during the island time. It was first demonstrated in [3] that different con- growth with a CCD camera and were stored on com- ditions of etching and oxide film growth can be created puter. The software package made it possible to record by varying the oxygen pressure and temperature. Quite diffraction patterns at a rate of 10 frames per second. recently, this technique was developed further when the The Ge growth rate was 10 monolayers (MLs) per formation of an ultrathin oxide layer was related to fur- minute. The temperature was varied from room temper- ther growth of an epitaxial silicon layer [4]. Prior oxi- ature to 700°C. Si(100) substrates were employed with dation of the silicon surface makes it possible to signif- a misorientation of less than 0.5°. Oxidation was per- icantly decrease germanium islands in size and increase formed in the MBE chamber at an oxygen pressure of their density. It was shown in [5, 6] that, when islands up to 10Ð4 Pa and a substrate temperature of 400Ð

78 NIKIFOROV et al.

d, ML 500°C. After pumping out the oxygen, germanium was –101234567 deposited on the oxidized surface. 8 3. RESULTS AND DISCUSSION 7 The growth of a Ge ﬁlm on an oxidized silicon sur- 6 face was monitored with the use of electron diffraction patterns by recording both the qualitative changes in 5 structure and morphology of a growing ﬁlm surface and

, % quantitative data on the elastic strain of the surface unit Si a 4 cell [7]. To analyze the initial stage of the Ge ﬁlm )/

Si growth on an oxidized silicon surface, we recorded the a 3 changes in intensity of the specular reﬂection and of the – ||

a three-dimensional electron reflection diffraction (3D ( 2 reflections). These reflections are very sensitive to changes in the surface roughness; in particular, the 1 appearance of a 3D reflection indicates the presence of three-dimensional objects on the surface under exami- 0 nation. In the case of film growth on a clean surface, oscillations of the specular reflection intensity, its van- –1 ishing, and the appearance of a 3D reflection when the 0 0.2 0.4 0.6 0.8 1.0 Ge film thickness becomes larger than four monolayers d, nm indicate layer-by-layer growth of the wetting layer followed by the formation of three-dimensional islands. In Fig. 1. Variations in the two-dimensional surface unit cell the case of Ge film growth on an oxidized surface, the parameter a|| during the Ge film growth on the oxidized Si(100) surface. intensity of these reflections changes even after deposition of one monolayer and no oscillation in the specular reflection intensity is observed. These features suggest that the wetting layer does not form on the oxidized surface. Indeed, as the first monolayer is deposited, an adsorbed germanium layer forms on the SiO2 surface and then transforms into three-dimensional islands when the next monolayers are deposited. Therefore, in the case of a Ge film growing on an oxidized silicon surface, the VolmerÐWeber mechanism is operative rather than the StranskiÐKrastanow growth mechanism, which operates in the case of a clean silicon surface. To analyze the Ge lattice strains, we determined the changes in the (two-dimensional) surface unit cell parameter a||. For this purpose, we recorded the variations in the distance between the diffraction pattern spots corresponding to the parameter a||. Figure 1 shows the change in a|| during the Ge film growth with respect 0 20 40 60 80 nm to the value of this parameter at the silicon surface. It can be seen from Fig. 1 that, as the film grows, the surface unit cell of the Ge lattice varies significantly with respect to that for Si, which remains constant. The vari- 1 ation reaches 7%, as in the case of a film growing on a , nm

h clean Si(100) surface [7]. In the beginning, elastically strained islands grow. Then, a|| decreases to the value characteristic of bulk germanium, which is indicative of 02040 60 80 nm complete plastic relaxation of the islands. Such a behavior of the parameter a|| is analogous to that in the Fig. 2. Scanning tunneling microscopic image of an array of case of germanium heteroepitaxy on a clean Si(100) Ge islands on a silicon oxide surface and the morphology surface, but in the former case the relaxation of strained change proﬁle along the light line; dGe = 3 MLs and Ts = Ge islands comes to a close much earlier and the three- 650°C. dimensional islands that form after the ﬁrst monolayer

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

GROWTH AND STRUCTURE OF Ge NANOISLANDS 79 ° this case (dGe = 3 MLs, Ts = 650 C) is shown in Fig. 3. It can be seen that not only small islands but also islands with dimensions that are larger by an order of 20 magnitude and with a significantly lower density are formed as the effective thickness of deposited germanium increases. Therefore, when the thickness of a ger- 15 manium film deposited on the oxidized Si(100) surface is greater than 1 nm, a bimodal distribution of islands in terms of size and density is observed. This conclusion 10 is also confirmed by electron-microscopic studies.

ACKNOWLEDGMENTS 5 This study was supported by the Russian Founda- tion for Basic Research, project nos. 03-02-16468 and 03-02-16506. 0 2 4 6 8 10 12 l, nm REFERENCES Fig. 3. Distribution of Ge islands in size at the bottom for d = 3 MLs and T = 650°C. 1. D. J. Eaglesham and M. Cerullo, Phys. Rev. Lett. 64, Ge s 1943 (1990). 2. A. I. Yakimov, A. V. Dvurechenskii, Yu. Yu. Proskurya- is deposited already have the maximal value of the two- kov, et al., Thin Solid Films 336, 332 (1998). dimensional surface unit cell parameter. Therefore, the 3. J. J. Lander and L. Morrison, J. Appl. Phys. 33, 2098 maximum elastic strain already exists in the nuclei of (1962). three-dimensional islands. 4. Y. Wei, M. Wallace, and A. C. Seabaugh, J. Appl. Phys. 81, 6415 (1997). Islands differ in size and density depending on the 5. A. A. Shklyaev, M. Shibata, and M. Ichikawa, Phys. Rev. thickness of the deposited germanium. For ﬁlm thick- B 62, 1540 (2000). nesses of up to 5 MLs, the dimensions of islands at the 6. A. Barski, M. Derivaz, J. L. Rouviere, and D. Buttard, bottom are less than 10 nm and their density is higher Appl. Phys. Lett. 77, 3541 (2000). × 12 Ð2 than 2 10 cm . Figure 2 shows a scanning tunneling 7. A. I. Nikiforov, V. A. Cherepanov, O. P. Pchelyakov, microscopic image of an array of Ge islands formed on et al., Thin Solid Films 380, 158 (2000). a silicon oxide surface after three germanium monolayers were deposited at a substrate temperature of 650°C. The distribution of Ge islands in size at their bottom in Translated by Yu. Epifanov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 80Ð84. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 83Ð87. Original Russian Text Copyright © 2004 by Teys, Talochkin, Romanyuk, Olshanetsky.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Growth of Germanium Nanoislands and Nanowires on Singular and Vicinal Si(111) Surfaces Prior to the Formation of a Wetting Layer S. A. Teys, A. B. Talochkin, K. N. Romanyuk, and B. Z. Olshanetsky Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia e-mail: [email protected]

Abstract—The growth of germanium nanoislands and nanowires on singular and vicinal Si(111) surfaces is investigated by scanning tunneling microscopy (STM). It is shown that the formation of a Ge wetting layer on the Si(111) surface at germanium deposition rates of approximately 10Ð3 BL/min and epitaxial temperatures of 350Ð500°C occurs through the island or multilayer growth mechanism. This makes it possible to prepare arrays of Ge islands with a height of 3 BL and a density of 109Ð1012 cmÐ2. The growth of Ge nanowires with a constant height and a width dependent on the Ge coverage is observed on vicinal Si(111) surfaces. It is found that the surface diffusion coefﬁcients of Ge adatoms on the Ge(5 × 5) surface are severalfold larger than those on the Si(7 × 7) surface. The Raman spectra of optical phonons on the Si(111) surface with Ge nanoislands 3 BL in height contain a number of lines associated with the quantization of the phonon spectrum along the [111] growth direction. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION in detail in our earlier work [9]. The growth of germa- The photosensitive and light-emitting properties of nium layers was carried out at temperatures of 350Ð ° Ð2 Ð3 structures with Ge islands on an Si(100) surface have 500 C and deposition rates of 10 Ð10 BL/min (1 BL = × 15 2 been intensively investigated in recent years [1Ð4]. The a0 = 1.44 10 atoms/cm is a bilayer of Ge atoms). growth of germanium layers on silicon substrates The STM images of the surface were obtained at room occurs through the StranskiÐKrastanov mechanism. In temperature. Tungsten tips prepared by electrolytic this case, the formation of a strained Ge wetting layer is etching in an alkaline solution served as STM probes. followed by the three-dimensional growth of Ge The Raman spectra of optical phonons were recorded islands. According to scanning tunneling microscopy on a DFS-52 spectrometer upon excitation with an Ar (STM), the homoepitaxial growth of silicon on the laser at wavelength λ = 488 nm. In order to avoid oxi- Si(111) surface at the initial stages [5] and the forma- dation of the growth surface, the structures grown were tion of a Ge wetting layer on the Si(111) surface [6Ð9] rapidly transferred in a nitrogen atmosphere from the proceed by the island mechanism. Nanoislands grow in growth chamber to a liquid-nitrogen cryostat. height and form second and third layers, which serves as an example of the growth through the multilayer mechanism [7, 10]. 3. RESULTS AND DISCUSSION In this work, we performed STM investigations of At the initial stages of heteroepitaxial growth, Ge the growth of germanium nanoislands and nanowires atoms are deposited in the form of clusters in halves of on singular and vicinal Si(111) surfaces at stages of the unit cells of the Si(7 × 7) surface structure [6, 9, 11]. An formation of a wetting layer and the onset of three- increase in the Ge amount on the surface leads to the dimensional growth of germanium islands at low coalescence of clusters and the formation of triangular growth rates. islands [6, 9, 12]. When the Ge epitaxial growth occurs at a temperature of 380°C and a rate of 4 × 10Ð3 BL/min, the density of clusters increases and, at a maximum, 2. EXPERIMENTAL TECHNIQUE exceeds the density of larger sized three-dimensional In our experiments, we used n-Si and p-Si samples islands by a factor of approximately 10 (Fig. 1). With (12 × 3 × 0.4 mm in size) with a resistivity of 5Ð10 Ω cm. a further increase in the Ge coverage to 0.5 BL, the The preparation of atomically clean surfaces, germa- clusters on the surface undergo complete decomposi- nium epitaxy, and STM observations were performed tion and give way to islands whose density (2 × on a RIBERÐOMICRON instrument under ultrahigh 1010 atoms/cm2) remains constant at coverages of less vacuum. The experimental conditions were described than 0.8Ð1.0 BL. At such low growth rates, the height

GROWTH OF GERMANIUM NANOISLANDS AND NANOWIRES 81

1013 (a) 1

12 –2 10

Density, cm 10

1010 0 0.2 0.4 0.6 Ge coverage, BL

Fig. 1. Density of (1) Ge clusters and (2) Ge islands on the Si(111) surface as a function of the Ge coverage. The growth temperature is 380°C, and the growth rate is 4 × − 10 3 BL/min. 0 400 800 nm of the majority of islands on Si(111) terraces reaches 3 (b) BL. The subsequent growth of islands proceeds only in the substrate plane until a continuous wetting layer is formed. A distinguishing feature of the self-assembled growth of nanoislands in the Ge/Si(111) system is that the island size is limited by a height of 3 BL. The reason for this limitation still remains unclear. However, with a high probability, this limitation can be associated with the speciﬁc features of the mechanisms of diffusion and incorporation of adatoms into the reconstructed surface of a diamond-like crystal lattice, because a similar growth at low deposition rates was observed during homoepitaxial growth of silicon on Si(111) [12]. The linear dependence of the logarithm of the island density on the epitaxial temperature indicates the kinetic limitation of island nucleation. Therefore, arrays of three-layer Ge islands with a density of 109Ð 1012 cmÐ2 can be grown on the Si(111) surface prior to the formation of a continuous wetting layer. 0 400 800 nm The growth of islands in height occurs through the migration of Ge atoms from the lower terrace to the Fig. 2. STM images of the surface after deposition of upper terrace, because the amount of Ge arriving at the 0.3-BL-thick Ge layers (temperature, 350°C; deposition island top is too small to provide the formation of the rate, 4 × 10Ð3 BL/min) on different initial surfaces: (a) the Si(111)-(7 × 7) surface and (b) the Si(111)-(7 × 7) surface second and third layers. The migration effect is the sec- × ond speciﬁc feature of the self-assembling of Ge atoms with a Ge(111)-(5 5) layer. on the Si(111) surface. The third feature responsible for × the self-assembling is the formation of the (7 7) sur- a coverage of approximately 3 BL (or at smaller cover- face structure on both the substrate and the surface of ages during growth at higher temperatures), the (5 × 5) growing islands. The lateral sizes of islands are multi- × structure is observed over the entire surface. Therefore, ples of the size of the (7 7) unit cell. The island edges × × coincide with the boundaries of the (7 × 7) cells. The the (7 7) structure transforms into the (5 5) structure surface structure plays an important role in the mass at the island tops. This transformation into the new sur- transfer along the surface. At a coverage of ~0.5 BL, the face structure results in a considerable increase in the (7 × 7) surface structure occupies approximately 70% rate of surface diffusion of adsorbed Ge atoms. This is of the island surface area, whereas the (5 × 5) structure qualitatively illustrated in Fig. 2, which shows the STM occupies only 30% of the island surface area. However, images of two different surfaces after Ge epitaxy at a when islands merge together into a continuous layer at temperature of 350°C. Figure 2a displays the STM

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

82 TEYS et al. tion of a depletion region (the region free of islands) Ge Si along the step. The depletion region on steps of the first type on the side of the upper terrace is larger than that on the lower terrace. This suggests a lower energy barrier to the incorporation of Ge atoms into the step on the side of the upper terrace. After Ge epitaxy on the surface with steps of the second type, the edges of initial steps remain smooth and a chain of merging islands is formed on the side of the upper terrace. We determined the regions of depletion in islands in the vicinity of steps and the width of Ge nanowires formed along the steps with a specially developed program for analyzing STM images. It was found that, for steps of the second type, the depletion region on the side of the lower terrace always exceeds the depletion region on the side of the upper terrace. Moreover, the number of Ge atoms incorporated into the step edge on the side of the lower terrace is less than that on the side of the upper terrace. These findings indicate that Ge atoms migrate from the lower terrace to steps of the second type on the upper 02040nmterrace. Fig. 3. STM image of the Ge nanowire with a height of 1 BL Thus, the mechanism of growth of perfect triangular and a width equal to the size of two (7 × 7) unit cells (tun- islands becomes clear. Germanium atoms migrate neling current, constant voltage, fixed distance to the sur- through steps of the second type to upper layers. As a face). result, Ge atoms from the upper and lower terraces are incorporated into steps of the first type. A rapid growth image of the surface after germanium deposition and disappearance of steps of the first type in islands directly on the clean Si(111) surface with a (7 × 7) and a continuous migration of Ge atoms to the second structure. The STM image of the surface after Ge epit- layer favor an increase in the island height. axy on the Si(111) substrate with a Ge(5 × 5) continu- If the epitaxial growth of germanium nanoislands ous layer (preliminarily deposited at 550°C) is repro- occurs on steps of the second type at high temperatures duced in Fig. 2b. It can be seen from these figures that under conditions where the amount of surface defects the densities of islands on the terraces differ by a factor decreases and the migration length of Ge atoms of ~40. In our opinion, a drastic increase in the migra- becomes comparable to the terrace width, the height of tion length leads to a qualitative change in the island Ge nanowires can reach 1 BL. Figure 3 displays an growth. The density of nuclei of new islands on the wet- STM image of the Si step with a Ge nanowire 1 BL in ting layer with a (5 × 5) structure decreases signifi- height, which was obtained in a tunneling current cantly despite numerous surface defects. mode. The formation of the Ge nanowire with a width equal to the size of two (7 × 7) unit cells suggests that It is revealed that vicinal Si(111) surfaces deviating the surface structure affects the self-assembled growth. from the (111) plane by several degrees involve steps It can be seen from Fig. 3 that, compared to the Ge with a height equal to the interplanar distance (1d111). nanoislands, the Ge nanowires are more perfect Upon the deviation in the opposite directions [112 ] and nanoobjects with constant width and height. The Ge growth along steps of height 3d111 is also of consider- [112 ], the step edges contain atoms with one dangling able interest. For these steps, the height of the grown Ge bond (steps of the first type) and atoms with two dan- nanowire is limited by 3 BL, as is the case with islands; gling bonds (steps of the second type), respectively. A moreover, the width of the nanowire depends on the smooth decrease in the temperature in the phase transi- coverage and is a multiple of the size of the (7 × 7) unit tion range on the surface with steps of the second type is cell. attended by the formation of steps 3 BL (3d ) in height 111 We also studied the Raman spectra of optical (in addition to steps of height 1d111). The fraction of steps 3d in height on the surface increases with an increase phonons on the Si(111) surface containing Ge islands 111 with a height of 3 BL and a density of approximately in the angle of deviation from the (111) plane [13]. 2 × 1010 cmÐ2 [14]. It was revealed that the Raman spec- Upon the interaction of Ge with steps of the first tra exhibit a series of phonon lines (Fig. 4). The vertical type, the initially smooth edge of the step acquires a arrow in Fig. 4 indicates the location of the peak sawtooth shape; i.e., steps of the first type are gradually assigned to triply degenerate phonons of bulk germa- replaced by steps of the second type. The incorporation nium at T = 77 K (305 cmÐ1). In our case, the dege- of Ge adatoms into the step edge results in the forma- neracy is removed by mechanical stresses in the

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

GROWTH OF GERMANIUM NANOISLANDS AND NANOWIRES 83

Ge/Si(111) system. The Ge islands are strained as a Ge/Si(111) result of compression in the (xy) growth plane and 4 T = 77 K Ge extension along the z growth direction. Since the lateral λ = 488 nm LO2 TO sizes of islands substantially exceed the height, the LO 1 effect of lateral faces can be ignored and the strain in 3 3 the (111) plane can be treated as homogeneous. The LO TO2 components of the strain tensor in the (111) growth 2 1 ε ε ε ε plane are designated as xx = yy = . The component zz σ can be determined from the boundary condition zz = 0, 1 where σ is the component of the stress tensor. By

zz Raman intensity, arb. units transforming the strain tensor in terms of the (100) sys- 0 220 240 260 280 300 320 tem and applying the Hooke law, we determine the –1 components of the stress tensor in this system. After the Frequency, cm inverse transformation with due regard for the boundary condition, we obtain the strain along the [111] Fig. 4. Raman spectrum of optical phonons on the Si(111) direction: surface with Ge nanoislands at a temperature of 77 K. ε ε ()() zz = Ð2 xx C11 + 2C12 Ð C44 / C11 ++2C12 2C44 = Ð0.92ε, where C11, C12, and C44 are the components of the elas- TO tic compliance tensor for germanium. The components LO of the stress tensor in the growth plane can be written in 310 the form σσ σ 300 ==xx yy ε()() = 3C44 C11 + 2C12 / C11 ++2C12 2C44 . 290 These stresses split the state of the optical phonon with the wave vector k = 0 into the singlet (LO) and triplet (TO) states. The expressions for the dependence –1 280 of the frequency of these phonons on the biaxial stress in a plane perpendicular to the (111) plane were derived in [15]: 270 Ω ω ∆Ω ()∆Ω L = 0 + h Ð 1/3 , (1) Frequency, cm Ω ω ∆Ω ()∆Ω 260 T = 0 ++h 2/3 , (2) ω where 0 is the frequency of optical phonons of germa- n = 2 Ge Si ∆Ω σ ω 250 n = 1 nium; h = 2 (S11 + 2S12)(p + 2q)/6 0 is the hydro- ∆Ω Ω static component of the frequency shift; = T Ð n = 3 Ω σ ω L = S44r/2 0 is the LOÐTO splitting; S11, S12, and S44 240 are the components of the elastic constant tensor; and p, 123456 q, and r are the anharmonicity constants of germanium. According to the experimental data obtained in [16], 230 the anharmonicity constants are as follows: p = − ω 2 − ω 2 ω 2 π π π 1.470 , q = 1.930 , and r = Ð1.080 . After substi- 0 1 2  -------------- ----- tuting numerical values of all the parameters into 3 a0 3 a0 a0 expressions (1) and (2), we have Wave number ∆Ω Ω ω εω T ==T Ð0 Ð 1.306 0, ∆Ω Ω ω εω Fig. 5. Dispersion curves for optical phonons in germanium L ==L Ð0 Ð 0.322 0. along the [111] direction. Dashed lines correspond to the ε results of calculations performed in [17]. Solid lines are the The strain is used as a ﬁtting parameter. dispersion curves obtained with allowance made for the The height of Ge islands is limited by h = 3 BL = strain of germanium island. Circles indicate the optical- 3a , which leads to a substantial change in the phonon phonon frequencies measured in Ge quantum dots. The 0 inset shows the dependences of the amplitude of atomic spectrum. The spectrum of phonons with wave vectors vibrations according to calculations within the model of a k along the [111] direction is quantized according to the one-dimensional chain.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 84 TEYS et al. condition for the formation of a standing wave: kn = phonons on the Si(111) surface with Ge nanoislands (π/h)n, where n is an integer. Consequently, there exist contain a series of phonon lines associated with the only three vibrational modes of TO and LO phonons quantization of the phonon spectrum along the [111] (n = 1, 2, 3) in the Brillouin zone. The inset to Fig. 5 growth direction. The strain of Ge nanoislands is deter- shows the vibration amplitudes of atoms (N) for three mined. longitudinal optical modes (n = 1, 2, 3) calculated in terms of the model of a one-dimensional chain consisting of six atoms. Within this model, it is assumed that ACKNOWLEDGMENTS the amplitude of atomic vibrations is equal to zero at This work was supported by the Russian Foundation N = 7 (i.e., at the interface with Si) and that the first for Basic Research (project nos. 01-02-16844-a, 03-02- atom has a dangling bond (i.e., it is located on a free 16506-a) and the Ministry of Industry, Science, and surface). Technology of the Russian Federation (state contract The dispersion curves for optical phonons of germa- no. 40.012.1.1.1153). nium in the first Brillouin zone in the [111] direction are depicted in Fig. 5. The circles indicate the experi- REFERENCES mental phonon frequencies that correspond to wave vectors k at n = 1, 2, and 3. The dashed lines are the 1. V. A. Markov, H. H. Cheng, Chih-ta Chia, et al., Thin n Solid Films 369, 79 (2000). dispersion curves calculated in [17] for optical phonons 2. O. P. Pchelyakov, Yu. B. Bolkhovityanov, A. V. Dvurech- of bulk germanium in the [111] direction. The solid enskii, et al., Thin Solid Films 367, 75 (2000). lines represent the dispersion curves calculated in [17] and shifted according to expressions (1) and (2). These 3. O. P. Pchelyakov, Yu. B. Bolkhovityanov, A. V. Dvurech- enskiœ, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) 34 shifts for TO and LO phonons are determined by the (11), 1281 (2000) [Semiconductors 34, 1229 (2000)]. quantities ∆Ω and ∆Ω . The strain ε was obtained from T L 4. K. Brunner, Rep. Prog. Phys. 65, 27 (2002). the best fit to the experimental frequencies. As a result, ε ± 5. U. Koehler, J. E. Demuth, and R. J. Hamers, J. Vac. Sci. the strain was estimated as = Ð0.029 0.003. This Technol. A 7, 2860 (1989). value slightly differs from the strain of Ð0.04, which 6. U. Koehler, O. Jusko, G. Pietsch, et al., Surf. Sci. 248, should correspond to the pseudomorphic growth of ger- 321 (1991). manium on silicon and was observed in Ge quantum dots grown on the Si(100) surface [18]. 7. B. Voigtlaender and A. Zinner, Surf. Sci. 351, L233 (1996). 8. N. Motta, A. Sgarlata, R. Calarco, et al., Surf. Sci. 406, 4. CONCLUSIONS 254 (1998). 9. S. A. Teys and B. Z. Olshanetsky, Phys. Low-Dimens. Thus, the results obtained in this work can be sum- Struct., Nos. 1Ð2, 37 (2002). marized as follows. The wetting layer in the Ge/Si(111) 10. J. Tersoff, A. W. Denier van der Gon, and R. M. Tromp, system at germanium deposition rates of approximately Phys. Rev. Lett. 72 (2), 266 (1994). Ð3 10 BL/min is formed through the island or multilayer 11. Y. P. Zhang, L. Yan, S. S. Xie, et al., Surf. Sci. 498, L60 growth mechanism. The Ge epitaxial growth at low ° (2002). rates and temperatures of 350Ð500 C provides the for- 12. B. Voigtlaender, Surf. Sci. Rep. 43, 127 (2001). mation of arrays of Ge islands with a height of 3 BL and 9 12 Ð2 13. J. Wei, X. S. Wang, J. L. Goldberg, et al., Phys. Rev. Lett. a density of 10 Ð10 cm on the silicon surface until a 68, 3885 (1992). continuous wetting layer is formed. The self-assembled 14. A. B. Talochkin and S. A. Teys, Pis’ma Zh. Éksp. Teor. growth of Ge nanoislands on the Si(111) surface is sub- Fiz. 75 (6), 314 (2002) [JETP Lett. 75, 264 (2002)]. stantially affected by the following factors: the migra- 15. I. I. Novak, V. V. Baptizmanskiœ, and L. V. Zhoga, Opt. tion of Ge atoms from the lower terrace to the upper ter- Spektrosk. 43, 252 (1977) [Opt. Spectrosc. 43, 145 race on steps of the second type, the limitation of the Ge (1977)]. nanoisland height to three bilayers, and the ordering 16. F. Cerdeira, C. J. Buchenauer, F. H. Pollak, and M. Car- effect of the (7 × 7) surface structure. An increase in the × dona, Phys. Rev. B 5, 580 (1972). rate of Ge surface diffusion upon formation of the (5 17. W. Weber, Phys. Rev. B 15, 4789 (1977). 5) structure on the surface of the wetting layer leads to a crossover of the mechanism of Ge island growth at 18. A. B. Talochkin, V. A. Markov, A. I. Nikiforov, and S. A. Teys, Pis’ma Zh. Éksp. Teor. Fiz. 70, 279 (1999) coverages of more than 3 BL. Smooth Ge nanowires [JETP Lett. 70, 288 (1999)]. whose width is a multiple of the size of the (7 × 7) unit cell and a height is 1 or 3 BL can be grown along steps of the second type. The Raman spectra of optical Translated by O. Borovik-Romanova

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 85Ð88. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 88Ð90. Original Russian Text Copyright © 2004 by Valakh, Dzhagan, Lytvyn, Yukhymchuk, Krasil’nik, Novikov, Lobanov.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Composition and Elastic Stresses in Multilayer Structures with Si1 Ð xGex Nanoislands M. Ya. Valakh*, V. N. Dzhagan*, P. M. Lytvyn*, V. A. Yukhymchuk*, Z. F. Krasil’nik**, A. V. Novikov**, and D. N. Lobanov** * Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, 03028 Ukraine ** Institute of Microstructure Physics, Russian Academy of Sciences, Nizhni Novgorod, 603600 Russia e-mail: [email protected]

Abstract—The composition and mechanical stresses in Si1 Ð xGex nanoislands involved in multilayer and single-layer structures grown under the same conditions are determined using Raman spectroscopy. It is demonstrated that an increase in the content of silicon in the nanoislands contained in a multilayer structure does not enhance their relaxation (as compared to that in a single layer) due to the absence of a free surface. The experimental scattering spectrum of folded acoustic phonons contains bands with sufﬁciently small half-widths, which indicates high quality of the grown superlattices with nanoislands. © 2004 MAIK “Nauka/Interperiod- ica”.

1. INTRODUCTION were grown for comparison. In the samples used in The majority of heterostructures exhibiting new AFM measurements, the upper layer of islands was not electronic and optoelectronic properties are based on coated with silicon. The Raman spectra were recorded IIIÐV semiconductors, which are widely used in mod- on a T64000 Jobin Yvon spectrometer equipped with a ern electronics built on well-developed and relatively CCD camera in the frequency range of optical vibra- cheap silicon technology. For purposes of increasing tions of the Si1 Ð xGex solid solution, and the phonon the operating frequency of microcircuits, integrating spectra were measured on a DFS-24 spectrometer with their elements into technological processes, and a photomultiplier and a system of photon counting in improving the emission efﬁciency, new functional prin- the low-frequency range. In the latter case, the sample ciples have been introduced into silicon electronics, for was under vacuum. An Ar+ laser with a wavelength of example, the use of quantum dots with a discrete energy 488 nm was used for excitation. The AFM investiga- spectrum [1Ð3]. One way to obtain arrays of quantum tions were performed on a Nanoscope III-a microscope dots is the self-assembled growth of germanium operating in tapping mode. nanoislands on a silicon substrate through the StranskiÐ Krastanov mechanism. The essence of this method is a crossover from the two-dimensional growth to the 3. RESULTS AND DISCUSSION three-dimensional growth of nanoislands due to a It is known that, in multilayer structures with quan- decrease in the elastic energy of the system. tum dots and a sufﬁciently thin spacer layer, the island growth is characterized by a vertical correlation due to In this work, multilayer structures with Si1 Ð xGex nanoislands were studied by Raman spectroscopy and the distribution of mechanical stresses in the spacer ε atomic-force microscopy (AFM) and the results layer [3Ð5]. The content x and the elastic strain of obtained were compared with available data for similar nanoislands can be determined from the Raman data, as single-layer structures. was shown in [6Ð8] for single-layer structures with self- assembled Ge/Si nanoislands. The frequency location of the bands in the Raman spectrum is related to the 2. SAMPLES AND EXPERIMENTAL TECHNIQUE content x and elastic strain ε by the expressions [6] ω ε The structures were prepared by molecular-beam GeÐGe = 282.5 + 16x Ð 385 , (1) epitaxy of germanium on an Si(001) substrate with a ω ε 250-nm-thick buffer silicon layer preliminarily grown GeÐSi = 400.4 + 14.2x Ð 575 , (2) on it. A germanium layer with a thickness of 7.5 mono- ω = 520.5 Ð 62x Ð 815ε. (3) layers (ML) was deposited on the buffer at a tempera- SiÐSi ture of 600°C, after which the islands formed were In order to determine the content x and elastic strain ε coated with a 26-nm-thick silicon layer. This procedure more correctly, it is necessary to estimate the effect was repeated six times. Similar single-layer structures exerted by other factors on the frequency location of the

86 VALAKH et al.

Ge–Ge As is known [9], the dependence of the frequency Ge–Si location of the GeÐSi vibration band on the content x is linear only in the range 0 ≤ x ≤ 0.4. In this connection, Si–Si we approximated this dependence for the unstrained SiGe solid solution by the second-degree polynomial in ≤ ≤ 1 the range 0.4 x 1. Taking into account the linear dependence of the frequency of this band on the elastic strain ε, we obtain the following relationship:

Intensity, arb. units ω = 387 + 81x Ð 78x2 Ð 575ε. (4) 2 GeÐSi After substituting the experimental frequencies of the 300 400 500 GeÐGe, GeÐSi, and SiÐSi vibrations (298.8, 416, and Raman shift, cm–1 496.5 cmÐ1, respectively) (Fig. 1, curve 1) and graphically solving the system of equations (1)Ð(4), as was Fig. 1. Raman spectra of (1) multilayer and (2) single-layer done by Groenen et al. [6], we found x = 0.6 and ε = structures with Si1 Ð xGex nanoislands. The contribution −0.015. A close value can be obtained from the ratio of from the silicon substrate to the spectrum is subtracted. the integrated intensities of the bands attributed to the GeÐGe and GeÐSi vibrations: IGeÐGe/IGeÐSi = x/2(1 Ð x).

Except for the Si1 Ð xGex nanoislands, the contribution to the Raman spectrum can be made by the GeÐGe vibrations in a thin wetting germanium layer and the SiÐGe vibrations at the interface between this layer and the silicon spacer layer [10]. However, according to the selection rules [11], scattering by a two-dimensional wetting layer in the scattering geometry 001(100, 100)001 used in our case is forbidden; moreover, the * thin transient SiGe layer formed at a growth temperature of 600°C substantially decreases the probability of exciting interfacial SiÐGe vibration modes. Intensity, arb. units In order to evaluate how the silicon spacer layer affects the parameters of the nanoislands, we studied a single-layer structure with Si1 Ð xGex nanoislands grown without a Si-cap layer. From analyzing the Raman –40 –20 0 20 40 spectra of this structure (Fig. 1, curve 2), we obtained Raman shift, cm–1 x = 0.75 and ε = Ð0.013. The higher content of silicon in nanoislands of the multilayer structure is explained Fig. 2. Stokes and anti-Stokes parts of the Raman spectrum by additional diffusion of silicon atoms from spacer of folded acoustic phonons of a multilayer structure with layers. This should result in a more efficient relaxation Si1 Ð xGex nanoislands. of elastic stresses. However, the nanoislands involved in multilayer structures are surrounded by silicon on all sides and, consequently, the relaxation is retarded. bands in the Raman spectrum. In our case, the effect of The low-frequency Raman spectrum of the multi- the spatial confinement of phonons on their frequencies layer structure under investigation exhibits a series of can be disregarded because of the sufficiently large size clearly defined equidistant bands (Fig. 2). For two- of the islands. According to transmission electron dimensional flat superlattices, these bands are associ- microscopy, the height of the islands is equal to 5Ð6 nm ated with scattering by folded acoustic phonons that and their lateral sizes are 50Ð70 nm. The contribution arise from the artificial periodicity in the growth direc- from the silicon substrate to the Raman spectrum of the tion [1, 12, 13]. As far back as 1956, Rytov [14] pro- single-layer structure can be subtracted. For multilayer posed a theoretical model for describing the phonon structures, this problem is complicated, because both spectrum of two-dimensional superlattices. More the substrate and all silicon spacer layers make a contri- recently, Milekhin et al. [15] used this model to advan- bution to the Raman spectrum. The occurrence of elas- tage in the case of superlattices with quantum dots. tic strains in these layers leads to a low-frequency shift Cazayous et al. [16, 17] proposed the mechanism ω of the SiÐSi vibration band with respect to its location responsible for Raman scattering in superlattices with in the spectrum for an unstrained silicon substrate. quantum dots irrespective of the number of layers in the However, this shift is small compared to the shift superlattices. According to their model, the low-fre- caused by elastic strains in real solid solutions of quency bands are observed upon interference of acous- islands with composition Si1 Ð xGex. tic phonons with a set of localized electron states. This

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

COMPOSITION AND ELASTIC STRESSES IN MULTILAYER STRUCTURES 87

qs fer insigniﬁcantly and, hence, the frequencies of the 50 doublets can be calculated by a simpliﬁed formula [13]: π ω 2 ± = V SL------mVSLqs, 40 d –1

2 2 Ð1/2 d d 1 d1d2 1 2 ------30 V SL = d ------2 ++------2 R + --- , R V 1V 2 V 1 V 2 ρ Raman shift, cm 20 V 1 1 R = ------ρ , V 2 2 ρ ρ 10 where 1 and 2 are the densities, d1 and d2 are the 0 0.2 0.6 1.0 thicknesses of the layers, V1 and V2 are the velocities of Wave vector, 10–6 cm–1 sound in the layers, and ω is the frequency of the phonon. Fig. 3. Theoretical dispersion curve for a multilayer structure with Si Ge nanoislands. The Raman spectra were calculated as a superposi- 1 Ð x x tion of two groups of phonons propagating in the growth direction through the islands and only wetting interference occurs with the participation of phonons of layers, respectively. It can be seen from the table that the whole Brillouin zone due to the breaking of transla- the theoretical frequencies of the acoustic phonons tional symmetry in the layers with nanoislands. The agree well with the experimental results. interference model allows one to determine not only the frequency locations of the peaks but also the fine structure of the lines and their intensity. In our calculations, 4. CONCLUSIONS we used the Rytov theory, because, as was demon- Thus, we investigated the influence of silicon spacer strated in [17], the frequency locations of the bands cal- layers on the composition and elastic stresses in culated in the framework of the interference model and Si1 − xGex nanoislands during the growth of multilayer the Rytov theory coincide for the structures containing island structures. The above analysis of the Raman no less than five to six layers of quantum dots. spectra demonstrated that the silicon content in a mul- It is known that the resultant dispersion curve for a tilayer structure with nanoislands increases as com- superlattice can be obtained by folding the initial pared to that in a single layer of nanoislands, whereas branch for the bulk material into a minizone with qmax = the residual elastic strain remains nearly unchanged. π/d, where d is the lattice constant. In the case when a The increase in the content of silicon in the nanoislands periodic structure scatters laser radiation with a wave is favorable for relaxation of mechanical stresses, but vector qs, the Raman spectrum exhibits doublets, the absence of a free surface in the nanoislands does not whose positions correspond to the points marked on the permit them to relax entirely. The experimental scatter- dispersion curve depicted in Fig. 3. According to the ing spectrum of folded acoustic phonons contains selection rules, this superlattice is characterized only by bands with sufficiently small half-widths, which indi- longitudinal acoustic phonons. The table presents the cates that the grown superlattices with nanoislands are experimental and calculated frequencies of these of high quality. The theoretically calculated frequencies π λ × of these bands agree well with the experimental results. phonons for the wave vector qs = 4 nλ/ = 1.14 106 cmÐ1, where λ is the wavelength of exciting laser radiation and nλ is the mean value of the refractive ACKNOWLEDGMENTS index of this structure (nλ = 4.33 for λ = 488 nm). For our structure, the acoustic impedances of the layers dif- This work was supported by the UkrainianÐRussian program “Nanophysics” and the International Associa- tion of Assistance for the promotion of cooperation Experimental and theoretically calculated frequencies of with scientists from the New Independent States of the folded acoustic phonons (in cmÐ1) in the Raman spectrum former Soviet Union, project no. INTAS 01-444. m +1 Ð2 +2 Ð3 +3 Ð4 +4 Ð5 REFERENCES Theory 14.7 15.1 24.7 24.9 34.6 35 44.6 45 1. V. V. Mitin, V. A. Kochelap, and M. A. Strocio, Quantum Heterostructures: Microelectronics and Optoelectronics Experiment 15 24.8 34.6 44.5 (Cambridge Univ. Press, Cambridge, 1999).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 88 VALAKH et al.

2. O. P. Pchelyakov, Yu. B. Bolkhovitnyakov, A. V. Dvure- 11. R. Schorer, G. Abstreiter, S. de Gironcoli, et al., Phys. chenskiœ, et al., Fiz. Tekh. Poluprovodn. (St. Petersburg) Rev. B 49 (8), 5406 (1994). 34 (11), 1281 (2000) [Semiconductors 34, 1229 (2000)]. 12. C. Colvard, T. A. Gant, M. V. Klein, et al., Phys. Rev. B 3. C. Teichert, Phys. Rep. 365, 335 (2002). 31 (4), 2080 (1985). 4. D. A. Tenne, V. A. Haisler, A. I. Toropov, et al., Phys. 13. A. B. Talochkin, V. A. Markov, Yu. A. Pusep, et al., Rev. B 61 (20), 13785 (2000). Superlattices Microstruct. 10 (2), 179 (1991). 5. O. G. Schmidt and K. Eberl, Phys. Rev. B 61 (20), 13721 (2000). 14. S. M. Rytov, Akust. Zh. 2 (1), 71 (1956) [Sov. Phys. Acoust. 2, 67 (1956)]. 6. J. Groenen, R. Carles, S. Christiansen, et al., Appl. Phys. Lett. 71 (26), 3856 (1997). 15. A. Milekhin, N. P. Stepina, A. I. Yakimov, et al., Eur. 7. Z. F. Krasil’nik, P. M. Lytvyn, D. N. Lobanov, et al., Phys. J. B 16, 355 (2000). Nanotechnology 13, 81 (2002). 16. M. Cazayous, J. Groenen, J. R. Huntzinger, et al., Phys. 8. A. V. Novikov, B. A. Andreev, N. V. Vostokov, et al., Rev. B 64, 033306 (2001). Mater. Sci. Eng. B 89, 62 (2002). 17. M. Cazayous, J. Groenen, A. Zwick, et al., Phys. Rev. B 9. J. C. Tsang, P. M. Mooney, F. Dacol, and J. O. Chu, 66, 195320 (2002). J. Appl. Phys. 75 (12), 8098 (1994). 10. S. De Gironcoli, E. Molinari, R. Schorer, and R. Abstre- iter, Phys. Rev. B 48 (12), 8959 (1993). Translated by O. Moskalev

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 89Ð91. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 91Ð93. Original Russian Text Copyright © 2004 by Sokolov, Deryabin, Yakimov, Pchelyakov, Dvurechenskiœ. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003)

Self-Assembling of Ge Quantum Dots in the CaF2/Ge/CaF2/Si Heteroepitaxial System and the Development of Tunnel-Resonance Diode on Its Basis L. V. Sokolov1, 2, A. S. Deryabin1, A. I. Yakimov1, O. P. Pchelyakov1, and A. V. Dvurechenskiœ1 1 Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia 2 Tomsk State University, Tomsk, 634050 Russia e-mail: [email protected]

Abstract—A CaF2/Ge/CaF2/Si(111) heteroepitaxial structure with Ge quantum dots was grown by molecular- beam epitaxy. A negative differential conductivity and conductivity oscillations caused by resonant hole tunneling were observed at room temperature. The energy spacing between the levels in quantum dots, as determined from the oscillation period, is 40Ð50 meV depending on the Ge dot size. © 2004 MAIK “Nauka/Inter- periodica”.

1. INTRODUCTION processing with deposition of a thin buffer oxide layer, the wafers were placed into an ultrahigh-vacuum cham- Low-dimensional objects, such as quantum dots ber of an MBE setup, where the substrate surface was (QD), which make it possible to study single-electron finally cleaned and a heterostructure was grown on it. and quantum effects, continue to attract the attention of Ge and CaF molecular beams were generated by cru- scientists. The smallest sizes, most attractive from the 2 cible sources; the CaF beam was formed through sub- viewpoint of physical effect detection, have been 2 achieved for QDs grown by self-assembling. To this limation of a bulk calcium fluorite crystal from a graph- end, Ge/Si and InAs/GaAs semiconductor heterojunc- ite crucible. The typical Ge and CaF2 growth rates were tions are most commonly used. Nanometer-sized ~0.16 and ~0.25 nm/s, respectively. During substrate objects have also been grown in dielectric hosts, e.g., preparation and epitaxial growth of the Ge and CaF2 films, the surface structure was monitored by using SiÐCaF2 [1] and SiÐSiO2 [2]. In the former case, the nanoobjects were thin silicon strips grown along atomic high-energy (~40 keV) electron diffraction (HEED) in the reflection geometry. The substrate was heated by steps on the CaF2 film surface, and in the latter, the nanoobjects were produced without using epitaxial radiation from a tantalum strip heater. technology. After Si surface cleaning, HEED showed a distinct It seems promising to employ the Ge/CaF hetero- diffraction pattern from the Si(111) 7 × 7 superstruc- 2 × junction for producing QDs [3]. CaF2 is characterized ture. This superstructure was changed by the (1 1) by a very wide band gap (~12 eV, which suggests structure immediately after deposition of the first CaF2 growth of deep quantum wells) and can be rather easily monolayer. The typical surface relief of a 10-nm-thick grown by molecular-beam epitaxy (MBE) on the CaF2 film is shown in Fig. 1. We can see that flat pyra- Si(111) surface. This makes it possible to use the mids consisting of atomically smooth terraces sepa- CaF2/Si(111) heterojunction as a substrate. CaF2 grown rated by monatomic steps arise on the CaF2 film sur- on a Si surface has cubic crystal structure and a lattice face. It can also be concluded that plastic relaxation of parameter close to that of silicon. For this reason, it can mismatch stresses begins even at this film thickness. be assumed that, as in the Ge/Si heterostructure, Ge This is indicated by the set of straight lines representing film epitaxy on the CaF2/Si heterostructure will be traces of glide dislocations. Their density is not high; accompanied by self-assembling of Ge nanoislands. therefore, the process of mechanical stress relaxation is at its initial stage.

2. EXPERIMENTAL The transverse electric transport in the produced structures can be studied if the layers containing Ge + As substrates of CaF2/Si heterostructures, p -type islands are tunnel-transparent for carriers. For this rea- Si(111) wafers were used. After conventional chemical son, we investigated ~2-nm-thick CaF2 ﬁlms. It was

90 SOKOLOV et al.

1 µm 1 µm

Fig. 1. Atomic-force microscopic pattern of the surface Fig. 2. Atomic-force microscopic pattern of a Ge/CaF2/Si relief of a CaF2 epitaxial ﬁlm. heterostructure with Ge islands.

ascertained that CaF2 films had better electric charac- quency of 15 Hz. Figure 4 shows the measured tunnel- teristics if they were grown in two stages. Films were ing current versus the voltage for two samples produced grown at a substrate temperature of ~520°C, and then under various conditions of Ge island growth. Both the samples were annealed at 700Ð750°C for an hour. curves feature regions of zero conductivity and quasi- Due to this procedure, the fluoride film resistivity periodic oscillations with periods ∆V ≈ 100 and 80 mV increased by three orders of magnitude up to ~109 Ω cm. for samples 131 and 120, respectively. Regions of neg- After a thin fluoride film was grown, an ensemble of ative differential conductivity are also clearly seen. The Ge islands formed on its surface. The substrate temper- structure of oscillations was fully reproduced in multi- ature in this process was 430Ð490°C. The HEED data ple bias-voltage sweeps. At the same time, oscillations showed that a Ge film has a smooth surface at the initial were entirely absent for similar samples containing no growth stage; islands arise at an average thickness of Ge QDs. ~3 nm. Their formation causes a sharp change in the Based on these data, it can be assumed that the con- HEED pattern. Point reflections characteristic of three- ductance oscillations observed are most likely caused dimensional diffraction from islands appear instead of by hole tunneling through the energy states in Ge the extended diffraction strands typical of a smooth islands, rather than by the single-particle charge effects. film surface. Atomic-force microscopy of the surface of such heterostructures also showed the presence of islands (Fig. 2). After the Ge island formation, a second, 2-nm-thick, CaF2 film was grown. Thereafter, the sample was Au annealed again at 700Ð750°C. At the final stage, a 20-nm-thick p+-type Ge layer was grown at the hetero- 20 nm p+-Ge structure surface to provide an ohmic contact for electric measurements. 2 nm CaF2 tunneling barrier Ge dots Electric measurements were carried out on mesas (see Fig. 3) 0.7 × 0.7 mm in size produced by plasma- chemical etching in the CF4 etchant. Gold areas depos- 2 nm CaF2 tunneling barrier ited onto the sample surface through vacuum evaporation served as a mask for etching and as top contacts. (111) p+-Si substrate

3. RESULTS OF ELECTRICAL MEASUREMENTS Au The differential conductance G = dI/dV of the grown two-barrier structures was measured at room temperature using the conventional two-point probe technique. Fig. 3. Structure of a tunnel-resonant diode based on the The applied voltage amplitude was ~1 mV at a fre- CaF2/Ge/CaF2/Si heterostructure (schematic).

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

SELF-ASSEMBLING OF Ge QUANTUM DOTS 91

0.8 120, respectively. The difference is caused by the different growth conditions and, hence, different QD T = 300 K sizes. The Ge ﬁlm in sample 120 was grown at 490°C, 0.6 Sample 120 while that in sample 131 was grown at 430°C. This decrease in temperature resulted in smaller island sizes and, hence, in an increased energy gap between the 0.4 quantum levels. By analogy with self-assembling Ge nanoislands on the Si(001) surface [5], it can be assumed that a distance of 40Ð50 meV between the 0.2 energy levels corresponds to Ge islands 10Ð15 nm in size on the CaF2/Si(111) surface. 0 In conclusion, it should be noted that the Sample 131 CaF /Ge/CaF /Si(111) heterostructures with self- Differential conductance, nS 2 2 assembling Ge QDs may be used as a basis for devel- –0.2 oping tunnel-resonant diodes operating at room temperature. –1.5 –0.50 0.5 1.5 Voltage, V ACKNOWLEDGMENTS Fig. 4. Bias-voltage dependences of the differential conduc- This study was supported by the Russian Founda- tance. tion for Basic Research, project no. 00-02-17900.

Certainly, the charge effects play an important role in REFERENCES tunneling experiments, where a moving charge carrier 1. V. Ioannou-Sougleridis, V. Tsakiri, A. G. Nassiopoulov, may be delayed in an island. This effect is possible in et al., Phys. Status Solidi A 165, 97 (1998). highly asymmetric tunneling junctions, in which the transmittance of the second (thicker) barrier is much 2. Y. Inoue and A. Tanaka, J. Appl. Phys. 86, 3199 (1999). lower than that of the ﬁrst (thinner) barrier [4]. Obvi- 3. A. I. Yakimov, A. S. Derjabin, L. V. Sokolov, et al., Appl. ously, this is not the case for the two-barrier structures Phys. Lett. 81 (3), 499 (2002). under study, in which both barriers have the same thick- 4. U. Meirav and E. B. Foxman, Semicond. Sci. Technol. ness. 10, 255 (1995). 5. A. V. Dvurechenskii, A. V. Nenashev, and A. I. Yakimov, In the case of a symmetric structure, the distance Nanotechnology 13, 75 (2002). between the conductance peaks should be equal to the double energy gap between the levels of QD hole states. This energy gap was 50 and 40 meV in samples 131 and Translated by A. Kazantsev

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 92Ð96. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 94Ð97. Original Russian Text Copyright © 2004 by Milekhin, Nikiforov, Ladanov, Pchelyakov, Schulze, Zahn.

PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Resonant Raman Scattering by Strained and Relaxed Germanium Quantum Dots A. G. Milekhin*, A. I. Nikiforov*, M. Yu. Ladanov*, O. P. Pchelyakov*, S. Schulze**, and D. R. T. Zahn** * Institute of Semiconductor Physics, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia e-mail: [email protected] ** Institut für Physik, Technische Universität Chemnitz, Chemnitz, D-09107 Germany

Abstract—This paper reports on the results of resonant Raman scattering investigations of the fundamental vibrations in Ge/Si structures with strained and relaxed germanium quantum dots. Self-assembled strained Ge/Si quantum dots are grown by molecular-beam epitaxy on Si(001) substrates. An ultrathin SiO2 layer is grown prior to the deposition of a germanium layer with the aim of forming relaxed germanium quantum dots. The use of resonant Raman scattering (selective with respect to quantum dot size) made it possible to assign unambiguously the line observed in the vicinity of 300 cmÐ1 to optical phonons confined in relaxed germanium quantum dots. The influence of confinement effects and mechanical stresses on the vibrational spectra of the structures with germanium quantum dots is analyzed. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION sitions of quantum dots, built-in mechanical stresses, etc.). Three-dimensional confinement of charge carriers In this work, the vibrational spectra of self-assem- in quantum dots and, as a consequence, the atomic-like bled structures with strained and relaxed germanium electron spectrum of these structures are responsible quantum dots were studied using resonant Raman scat- for their electronic and optical properties, which differ tering. substantially from those of bulk materials. Owing to the great variety of interesting properties revealed in these objects during numerous experiments, they are very 2. SAMPLES AND EXPERIMENTAL TECHNIQUE promising materials for use in the design of microelectronic and optoelectronic devices with improved char- The structures with germanium quantum dots were acteristics. Multilayer nanostructures, such as Ge/Si prepared by molecular-beam epitaxy of germanium and silicon layers on Si(001) substrates. The Ge/Si struc- and Ge/SiO2, are of special interest due to their possible application in various devices and integration with tures with strained germanium quantum dots were modern silicon technology. Among the large number of grown through the StranskiÐKrastanov method. The techniques devised for preparing structures with quan- growth temperatures of the silicon layer prior to and after the deposition of the germanium layer were equal tum dots, the most efficient method is the self-assem- ° bled growth of nanostructures in the course of molecu- to 800 and 500 C, respectively. The layers of germanium quantum dots were grown at a temperature of lar-beam epitaxy. This approach is based on the Stran- ° skiÐKrastanov growth mechanism, according to which 300 C. The thickness and the structure of the films the deposition of a material whose lattice parameter grown were controlled using reflection high-energy differs significantly from that of the substrate leads to electron diffraction (RHEED) patterns. The samples the formation of an array of strained nanoislands. In used in the measurements consisted of ten pairs of ger- recent years, self-assembled growth has been used to manium and silicon layers with nominal thicknesses produce relaxed quantum dots. It has been found that, dGe = 1.4 nm and dSi = 37 nm (in what follows, the nom- for the Ge/Si system, the deposition of a nanometer- inal thickness of a layer will be referred to as the thick- thick intermediate layer of silicon oxide prior to the ness). As was shown in our previous work [2], the mix- epitaxial growth of the germanium layer results in the ing of silicon and germanium atoms for these thick- formation of relaxed germanium quantum dots with a nesses of the layers is insignificant. size of less than 7 nm [1]. As has been shown recently, The structures with relaxed germanium quantum Raman scattering spectroscopy is a nondestructive dots were grown at a substrate temperature of 600°C on method providing information on the structural param- a silicon oxide layer. This layer was preliminarily eters of quantum dots (dispersion of sizes and compo- formed on the silicon substrate immediately in a growth

RESONANT RAMAN SCATTERING 93

T = 295 K Si substrate Ei = 2.41 eV z(x, y)z-

(a) 6 nm ˜ ˜ ˜ Ge–Ge ˜

(b) 6 nm Raman intensity, arb. units Ge–Si Fig. 1. HRTEM images of the transverse sections of the samples: (a) layer of strained Ge/Si quantum dots and (b) layer of relaxed Ge quantum dots. a chamber at a temperature of 500°C and an oxygen pressure of 2 × 10Ð4 Pa. For our experiments, we prepared b two samples with germanium layer thicknesses of 1 and 300 400 500 2 nm. In order to prevent oxidation of the quantum dots, Raman shift, cm–1 the sample surface was coated with a 10-nm-thick layer of amorphous silicon. The experiments on Raman scattering were carried Fig. 2. Raman spectra of the structures with germanium quantum dots grown on (a) a thin SiO2 layer and (b) an Si out in the geometries z(x, x)z and z(x, y)z , where the x, layer. y, and z axes are oriented along the [100], [010], and [001] crystallographic directions, respectively. The excitation was provided by Ar+, Kr+, and HeÐNe lasers 1012 cmÐ2. An analysis of the HRTEM data revealed with lasing lines in the wavelength range 676.4Ð that large-sized (100Ð200 nm) germanium islands with 457.9 nm (1.83Ð2.71 eV). The light scattered was a density of 7.3 × 107 cmÐ2 are formed in addition to the recorded in a backward scattering geometry with the germanium quantum dots. use of a Dilor 800-XY triple monochromator equipped with a CCD camera for multichannel detection. The Figure 2 shows the Raman spectra of relaxed and Ð1 strained germanium quantum dots. The Raman spec- spectral resolution was 1.5 cm . trum of the structures with relaxed germanium quantum dots exhibits an intense peak at a frequency of 3. RESULTS AND DISCUSSION 297 cmÐ1, which is attributed to Raman scattering by optical phonons conﬁned in quantum dots. In the The structural parameters of the germanium quan- Raman spectrum of the Ge/Se structures, the Raman tum dots were determined from high-resolution trans- Ð1 mission electron microscope (HRTEM) images of the scattering line is observed at a frequency of 315 cm transverse sections of the samples. Figure 1 displays corresponding to the frequency of longitudinal optical the atomically resolved images of the transverse sec- (LO) phonons in pseudomorphic germanium quantum dots [3]. The spectral features revealed in the vicinity of tions of the samples containing strained and relaxed Ð1 quantum dots. According to the HRTEM data, the 400 and 520 cm are associated with the GeÐSi vibra- Ge/Si quantum dots are typical hut clusters whose base tion modes and optical phonons in the silicon substrate and height are equal to 15 and 1.5Ð2 nm, respectively. due to light scattering, respectively. The density of Ge/Si quantum dots amounts to 3 × As it has been already noted in the literature, partic- 1011 cmÐ2, and the homogeneity is 20%. The germa- ularly by Kolobov [4], the Raman spectra of single- Ð1 nium quantum dots grown on the SiO2 surface have a crystal Si(001) exhibit a peak in the vicinity of 300 cm hemisphere-like shape with a base ranging from 4 to due to second-order Raman scattering by transverse 6 nm and a height from 3 to 4 nm. The density of ger- acoustic phonons at the X and (or) Σ points of the Bril- manium quantum dots is approximately equal to 2 × louin zone. This can lead to erroneous interpretation of

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

94 MILEKHIN et al. the Raman spectra of the Ge/Si nanostructures with 2.18 eV relaxed germanium quantum dots. Moreover, it is nec- Ge phonon essary to distinguish between the influence of mechanical stresses arising in the structures with strained ger- (a) manium quantum dots and the influence of confinement 2.41 effects of the phonons on the frequency position of the line in the spectrum of Raman light scattering by phonons in germanium quantum dots. The confinement 2.47 of phonons leads to a low-frequency shift in the position of the line attributed to optical phonons in the Raman spectrum of germanium quantum dots with respect to its position in the spectrum of the bulk ger- 2.54 manium, whereas the mechanical stresses arising in the quantum dots bring about a high-frequency shift. One possible way to separate the contributions to Raman scattering from the germanium quantum dots and the Intensity, arb. units 2.63 silicon substrate, to determine the mechanical stresses in quantum dots, and to elucidate the role played by the confinement effect in Raman light scattering by 2.66 phonons is to analyze the spectra of resonant Raman scattering in the materials under investigation. Raman spectra measured for different excitation energies in the scattering geometry z(x, y)z are shown in Fig. 3. It can be seen from Fig. 3 that, as the laser excitation energy increases, the line associated with 270 285 300 315 –1 optical phonons confined in the germanium quantum Raman shift, cm dots shifts toward the low-frequency range and becomes increasingly broader. This shift cannot be LO Ge phonon explained by the changes in the strained state in quantum dots of different sizes, because the magnitude of (b) mechanical stresses does not depend on the quantum dot size [5]. The contribution of the mechanical stresses can be excluded completely in the experiments on Raman scattering under resonance conditions for structures with relaxed quantum dots. 1.83 eV Figure 4 shows the dependences of the Raman intensity and the frequency of LO phonons in germa- 2.34 nium quantum dots on the excitation energy obtained from the data presented in Fig. 3. An analysis of the dependences of the intensity and the frequency position 2.41 of the Raman scattering line in the spectrum on the excitation energy allows us to draw an unambiguous 2.5 conclusion regarding the nature of the Raman scatter- Raman intensity, arb. units 2.54 ing peak. The frequency position of the line associated with optical phonons (315 cmÐ1) that are confined in hut 2.61 clusters under nonresonance conditions (1.83 eV) corresponds to the pseudomorphic state of germanium, whereas the frequency of optical phonons in relaxed germanium quantum dots (300 cmÐ1) coincides with the frequency of optical phonons in the bulk germanium. 2.71 The frequency position of the line attributed to optical 300 310 320 330 phonons confined in the germanium quantum dots Raman shift, cm–1 shifts toward the low-frequency range with an increase in the excitation energy from 2.5 to 2.7 eV. For struc- Fig. 3. Raman spectra of (a) relaxed and (b) strained structures with germanium quantum dots measured in the scat- tures with strained and relaxed germanium quantum Ð1 tering geometry z(x, y)z at different excitation energies. dots, these shifts are equal to 4Ð5 and 10 cm , respec- The thickness of the germanium layer is 1 nm. The vertical tively, which suggests a size distribution of the quantum solid line indicates the frequency position of the line dots. assigned to optical phonons in bulk germanium. PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

RESONANT RAMAN SCATTERING 95

The dependence of the Raman intensity on the exci- (a) tation energy exhibits a maximum in the range 2.2Ð (a) 300 2.4 eV. The considerable broadening of the resonance –1 peak (0.4 eV) can be explained by the fact that there is 295 a contribution from several resonances. The highest Raman intensity observed for relaxed quantum dots at 290 an excitation energy of 2.35 eV (with a germanium layer thickness of 1 nm) corresponds to the E0 reso- 285 nance in germanium quantum dots. The energy of the E resonance is equal to 0.9 eV for bulk germanium and 0 280 reaches 2.5 eV for germanium quantum dots due to the Raman intensity, arb. units confinement effect [6]. For a greater thickness of the Ge phonon frequency, cm 275 germanium layer (2 nm), the maximum shifts toward 1.8 2.0 2.2 2.4 2.6 the high-energy range (2.42 eV), which indicates the Energy, eV formation of germanium quantum dots of a smaller size. The specific feature observed at an energy of (b)(b) 315 –1 2.2 eV is most likely caused by the E1 transition in relaxed quantum dots. 312 For strained germanium quantum dots, the maximum in the dependence of the Raman intensity on the excitation energy is close to the resonance at an energy 309 of 2.34 eV observed by Kwok et al. [7]. This maximum is associated with the E1 transition. Under biaxial compressive stresses, the energy of the E1 transition 306 increases by 0.16 eV as compared to that for the bulk Raman intensity, arb. units material (2.23 eV). The E resonances in the wetting Ge phonon frequency, cm 0 303 germanium layer (2.0Ð2.2 eV) and in the germanium 1.8 2.0 2.2 2.4 2.6 quantum dots (2.4Ð2.6 eV) can also contribute to the Energy, eV resonant Raman scattering, which results in broadening of the spectral feature. Fig. 4. Dependences of the Raman intensity and the fre- For small-sized quantum dots, in which the elec- quency of optical phonons in germanium quantum dots on tronic states possess a higher energy, the Raman inten- the excitation energy: (a) structures containing germanium quantum dots grown on a thin SiO2 layer with germanium sity increases after the laser excitation energy reaches layer thicknesses of 1 nm (squares) and 2 nm (triangles) the value corresponding to the E0 resonance. Since the [Raman measurements are performed in the scattering quantum dots are characterized by a size distribution, it geometry z(x, y)z ], and (b) Ge/Si structures measured in the is most probable that, under nonresonance conditions, scattering geometries z(x, y)z (open symbols) and z(x, x)z it is these large-sized quantum dots (for which the con- (closed symbols). finement effect is negligible) that make a dominant contribution to Raman scattering. As the excitation energy increases above 2.3 eV, the small-sized quantum dots fined in this cavity: q = (0.25 ± 0.05)/a. The first optical are involved in the Raman scattering. For these quan- mode localized in the germanium quantum dots satis- tum dots, the confinement effect of optical phonons is fies the equation 2hcosα = π/q. Here, h and α are the rather significant and manifests itself in a decrease in quantum dot height and the angle between the base and the frequency of optical phonons observed in the the face of the pyramid, respectively. The quantum dot Raman spectra. For relaxed quantum dots, this shift height, which is determined from this expression, is exceeds the value characteristic of structures with equal to 0.9 ± 0.2 nm. Therefore, the germanium quan- strained quantum dots, which indicates a smaller size of tum dots involved in Raman scattering at an energy of relaxed quantum dots. 2.71 eV have a height of 0.7 nm and a base of 9 nm. From analyzing the frequencies of the optical The mean size of relaxed quantum dots contributing phonons, we can determine the mean size of germa- to the Raman scattering was estimated under the nium quantum dots that contribute to the Raman scat- assumption that the quantum dots are spherical in tering. As was shown by Talochkin et al. [6], the optical shape. The phenomenological model proposed by phonons confined in germanium quantum dots undergo Campbell and Fauchet [8] was also used to calculate elastic reflection at the heteroboundaries between the the spectrum of Raman scattering by spherical quantum Ge/Si faces and the base of pyramidal quantum dots dots of different sizes in the frequency range of optical forming a cavity. From the standard dispersion relation phonons. The mean size of quantum dots was deter- for optical phonons in germanium quantum dots, we mined from the comparison of the frequency position can obtain the wave vector of the optical phonons con- and the half-width of the line of Raman scattering by

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 96 MILEKHIN et al. optical phonons in the calculated and experimental International Association of Assistance for the promo- spectra. As a result, we found that the mean sizes of tion of cooperation with scientists from the New Inde- quantum dots predominantly contributing to the Raman pendent States of the former Soviet Union, project no. scattering spectra recorded at excitation energies of INTAS 01-0444. 2.18, 2.41, 2.47, 2.54, 2.63, and 2.66 eV are equal to 7.5, 5, 4, 3, 2.2, and 2 nm, respectively. REFERENCES 1. A. A. Shklyaev, M. Shibata, and M. Ichikawa, Phys. Rev. 4. CONCLUSIONS B 62, 1540 (2000). Thus, structures with strained and relaxed germa- 2. A. G. Milekhin, A. I. Nikiforov, O. P. Pchelyakov, et al., nium quantum dots were grown by molecular-beam Eur. Phys. J. B 16, 355 (2002). epitaxy. The shape and size of the quantum dots were 3. A. Milekhin, S. Schulze, D. R. T. Zahn, et al., Appl. Surf. determined using high-resolution transmission electron Sci. 175Ð176, 629 (2001). microscopy and Raman scattering spectroscopy. The 4. A. V. Kolobov, J. Appl. Phys. 87, 2926 (2000). use of resonant Raman scattering, which is selective 5. A. V. Nenashev and A. V. Dvurechensky, JETP 91, 497 with respect to quantum dot size, made it possible to (2000). assign unambiguously the Raman scattering lines to 6. A. B. Talochkin, V. A. Markov, A. I. Nikiforov, and optical phonons in germanium quantum dots and to S. A. Teys, Pis’ma Zh. Éksp. Teor. Fiz. 70, 279 (1999) elucidate the inﬂuence of conﬁnement effects and [JETP Lett. 70, 288 (1999)]. mechanical stresses on the vibrational spectra of struc- 7. C. H. Kwok, P. Y. Yu, C. H. Tung, et al., Phys. Rev. B 59, tures containing quantum dots. 4980 (1999). 8. I. H. Campbell and P. M. Fauchet, Solid State Commun. ACKNOWLEDGMENTS 58, 739 (1986). This work was supported by the Russian Foundation for Basic Research (project no. 02-02-17746) and the Translated by N. Korovin

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004

Physics of the Solid State, Vol. 46, No. 1, 2004, pp. 97Ð100. Translated from Fizika Tverdogo Tela, Vol. 46, No. 1, 2004, pp. 98Ð101. Original Russian Text Copyright © 2004 by Andreev, Krasil’nik, Kryzhkov, Yablonskiœ, Kuznetsov, Gregorkiewicz, Klik. PROCEEDINGS OF THE CONFERENCE DEDICATED TO O. V. LOSEV (1903Ð1942) (Nizhni Novgorod, Russia, March 17Ð20, 2003) Er3+ Photoluminescence Excitation Spectra in Erbium-Doped Epitaxial Silicon Structures B. A. Andreev*, Z. F. Krasil’nik*, D. I. Kryzhkov*, A. N. Yablonskiœ*, V. P. Kuznetsov**, T. Gregorkiewicz***, and M. A. J. Klik*** *Institute of the Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950 Russia e-mail: [email protected] **Physicotechnical Research Institute, Lobachevskiœ Nizhni Novgorod State University, Nizhni Novgorod, 603950 Russia ***Van der WaalsÐZeeman Institute, University of Amsterdam, The Netherlands

Abstract—Excitation spectra of erbium photoluminescence (λ = 1540 nm) in Si : Er epitaxial structures were studied within a broad pump wavelength range (λ = 780Ð1500 nm). Erbium photoluminescence was observed to occur at pump energies substantially less than the silicon band-gap width. Possible mechanisms of erbium ion excitation in this pump radiation energy region are discussed. © 2004 MAIK “Nauka/Interperiodica”.

1. INTRODUCTION poorly studied. This stimulated the present study of the excitation of erbium photoluminescence (PL) under We are presently witnessing a search for ways to variation of the pump photon energy in SMBE-grown integrate various optoelectronics devices, such as semi- Si : Er structures containing a variety of optically active conductor lasers, light-emitting diodes, photodetectors, erbium centers. radiation modulators, etc., with silicon microstructure technologies. Erbium-doped silicon has become a subject of considerable interest because the wavelength of 2. EXPERIMENT 4 4 its radiative transition I13/2 I15/2 in the 4f shell of Erbium-doped silicon structures were SMBE- the Er3+ ion (1540 nm) lies in the spectral region of grown on n- or p-type [100]-oriented Si substrates with maximum transparency and minimum dispersion of an electrical resistivity ρ ~ 10Ð20 Ω cm with the use of quartz optical-ﬁber communication lines. Application a Si : Er crystal source. The thickness of the epitaxial of sublimation molecular-beam epitaxy (SMBE) [1] to structures studied varied from 1.8 to 5.5 µm. The the growth of erbium-doped silicon layers makes it pos- growth temperature was varied from 500 to 600°C. As sible to produce uniformly and selectively doped Si : Er follows from SIMS measurements, the structures thus and SiGe : Er structures with a close-to-perfect crystal grown contained up to 5 × 1018 cmÐ3 Er atoms, 5 × lattice which exhibit strong erbium photo- and elec- 1019 cmÐ3 O atoms, and from 4 × 1018 to 1 × 1019 cmÐ3 troluminescence [2]. Minimization of the temperature C atoms. quenching of the luminescence in the Si : Er/Si struc- The photoluminescence spectra were measured tures is currently an important issue. This accounts for with a BOMEM DA3 high-resolution Fourier spec- the interest attracted, in particular, by silicon structures trometer. The PL signal was registered on a liquid- with optically active erbium centers in SiO -like pre- 2 nitrogen-cooled germanium detector (Edinburgh cipitates, which feature relatively weak thermal Instruments). The PL was studied at 4.2 K using a quenching [3]. closed-cycle optical cryostat. Optical pumping in the Excitation of erbium ions in silicon via the electron visible region required for investigation of the erbium subsystem of the semiconductor is known to be a much PL spectra was provided by cw Ar+ and Kr+ lasers with more efﬁcient mechanism than direct optical pumping an output power of up to 300 mW. of Er ions in dielectric matrices (the excitation cross A near-IR investigation of erbium PL excitation section of the Er3+ ion in silicon varies in different pub- spectra in the Si : Er/Si structures (780Ð1500 nm) was lications from 3 × 10Ð15 [4] to 10Ð12 cm2 [5], which is made with an optical parametric oscillator pumped by many orders of magnitude larger than the optical a pulsed Nd : YAG laser (355 nm). The pump pulse excitation cross section of erbium in a SiO2 matrix, duration was 5 ns, the pulse repetition frequency was 10−21 cm2). At the same time, it is universally accepted 20 Hz, and the maximum pulse energy was 7 mJ at a that energy transfer via the electronic subsystem of sil- wavelength of 780 nm. Thus, the maximum pulse icon is a complex multistage process involving impu- power was as high as 106 W. The PL signal was mea- rity levels in the silicon band gap and still remains sured with a grating spectrometer, a germanium detec-

98 ANDREEV et al.

3 2.5 4 H11/2 E 4 → 4 4S g CB I15/2 I9/2 3/2 2 4F 2.0 9/2 e Er3+ 4 I9/2 4 2 I13/2 4 1.5 ν I11/2 h ex < Eg PL , eV 4 E 1 h I15/2 4I VB 13/2 1.0 0 m µ 1

4 1.54 0 I15/2 0.5 Si:Er3+ Erbium PL internsity, arb. units

Erbium PL intensity, arb. units 4 → 4 0 I15/2 I11/2 1000 1100 1200 1300 1400 1500 0 Excitation wavelength, nm 800 90 1000 1100 Excitation wavelength, nm Fig. 2. Erbium PL excitation spectrum (λ = 1540 nm) Fig. 1. Erbium PL excitation spectrum (λ = 1540 nm) of a obtained at pump photon energies below Eg. Inset schemat- Si : Er structure at T = 10 K. Inset shows the energy level ically shows the proposed mechanism of erbium ion excita- 3+ ν scheme of the Er ion 4f shell. tion in silicon for h ex < Eg. tor, and a digital oscillograph (TDS 3032 Tektronix). transitions from the ground to upper excited states of λ 4 The excitation spectra of the erbium PL were recorded the erbium ion ( = 800 and 980 nm for the I15/2 at 10 K using a closed-cycle cryostat (Oxford Instru- 4 4 4 I9/2 and I15/2 I11/2 transitions, respectively). It was ments). found that excitation spectra of the erbium PL do not λ have any features at these values of wavelength ex 3. RESULTS AND DISCUSSION either in structures with Er ions in SiO2-like precipitates or in structures with single erbium centers (Fig. 1). We analyzed the contributions from various Er- This observation indicates that the efﬁciency of direct based optically active centers to the PL signal of the optical pumping of Er3+ ions in erbium-doped silicon Si : Er/Si structures using high-resolution Fourier spec- structures is extremely low, which makes energy trans- troscopy. At low temperatures, the PL spectra are dom- fer via the electronic subsystem of the silicon matrix a inated, depending on the actual growth conditions and dominant mechanism of erbium PL excitation in the post-growth annealing of the structures, by either Si : Er/Si structures, including structures with SiO -like narrow peaks of high-symmetry single erbium centers 2 precipitates. or a broad line (~30 cmÐ1) originating from the emission of an erbium ion in SiO2-like precipitates, which Figures 2 and 3 present excitation spectra of the form in silicon layers with a high oxygen content at erbium PL measured at temperature T = 10 K at various high growth temperatures (~600°C). The characteristic pump energies. At a low pumping power (P ~ 104 W), broadening and shift of the erbium PL spectrum to the erbium PL intensity was observed to decrease shorter wavelengths suggest that erbium ions in SiO2- monotonically with a decrease in the pump photon like precipitates provide a dominant contribution to the energy to a level close to the silicon band gap. This drop PL signal at high measurement temperatures. in the intensity is associated with a decrease in the It is universally accepted that erbium PL in Si : Er absorption coefﬁcient of silicon in the wavelength structures can be excited only by band-to-band pump- region in question and, as a consequence, a decrease in ing (photons with energies above the silicon band gap), the intensity of electronÐhole pair generation. Never- which generates electronÐhole pairs; after this, the car- theless, a noticeable erbium PL signal was observed at pump photon energies substantially lower than the sili- riers recombine and transfer the energy to the erbium λ ions. It may thus be assumed that the erbium PL excita- con band gap width ( = 1060 nm) down to the energy 3+ tion spectra in Si : Er structures should depend on the of the Er radiative transition (λ = 1540 nm) (Fig. 2). type of optically active erbium centers and the pump 5 6 λ As the pump power increases (P ~ 10 Ð10 W), a wavelength. We considered here the interval ex = 780Ð strong broad peak appears in the excitation spectrum of 1500 nm, which includes photon energies substantially the erbium luminescence whose maximum lies at less than the silicon band gap (λ ≈ 1060 nm). λ wavelength ex ~ 1030 nm (Fig. 3). It should be pointed We estimated the probability of direct optical pump- out that the high-energy edge of the peak coincides in ing of erbium ions in Si : Er structures with SiO2-like position with the absorption edge of radiation in bulk precipitates at exciting wavelengths corresponding to silicon. Thus, a sharp increase in erbium PL is observed

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 Er3+ PHOTOLUMINESCENCE EXCITATION SPECTRA 99 when the sample becomes optically transparent for the 0.9 exciting radiation. This feature implies, in particular, an 1030 nm Eg p = 0.004 extremely high efﬁciency of erbium PL excitation in 0.03 λ this spectral region ( ex ~ 1030 nm), because only a 0.7 0.10 small part (less than 1%) of the pump power is absorbed 1100 nm 0.24 in the sample in these conditions to contribute to the PL 980 nm 0.55 0.5 excitation. 1.00 Figure 4 displays PL spectra for three pump wave- p = P/P λ max lengths ( ex = 980, 1030, 1100 nm, speciﬁed by arrows 0.3 P ~ 106 W in Fig. 3) obtained at the maximum pump power (P = max 106 W). The PL spectra obtained feature the same character typical of the spectra of erbium PL in structures 0.1 Erbium PL intensity, arb. units with SiO2-like precipitates. This provides supportive 0 evidence that the PL signal observed for λ > 1060 nm 800 900 1100 1300 1500 ex Excitation wavelength, nm ν 3+ (i.e., for h ex < Eg) is nothing else than the PL of Er ions. Fig. 3. Erbium PL excitation spectra (λ = 1540 nm) The appearance of a noticeable erbium lumines- obtained at various pump power levels. cence signal under excitation by photons with an energy substantially lower than the band gap width cannot be assigned to the existence of density-of-states 0.6 tails in the silicon band gap, because the PL excitation λ ex = 980 nm spectra measured in [6] for the radiation of free and λ ex = 1030 nm bound excitons in silicon with boron and phosphorus λ λ ex = 1100 nm impurities exhibit a red cutoff at ex not over 1080 nm 0.4 at donor and acceptor concentrations up to 1019 cmÐ3. At the same time, the shallow-impurity concentration in our samples did not exceed 1018 cmÐ3. One could attempt to interpret this result by assum- 0.2 ing the electronÐhole pairs to be generated in two-photon transitions in the silicon matrix. In this case, however, the PL intensity would have to be quadratically Erbium PL intensity, arb. units dependent on the pump power, whereas the relation 0 observed experimentally followed a sublinear pattern 1525 1535 1545 1555 1560 (Fig. 5). Furthermore, the presence of two-photon Wavelength, cm–1 absorption cannot account for the peak in the erbium ion excitation spectra at pump photon energies close to Eg. Fig. 4. Erbium PL spectra measured at various values of the λ A more plausible interpretation of the observation pump radiation wavelength ex. ν of erbium PL for h ex substantially lower than Eg can be proposed in assuming that, in the silicon band gap in the structures under study, there are impurity levels that are 0.6 related to Er ions in the epitaxial layer. Indeed, erbium- doped silicon layers are known to have, as a rule, n-type conduction [1]. In this case, the absorption of a photon ν 0.4 of energy h ex < Eg would be capable of promoting electrons from the valence band directly to the donor levels associated with erbium, with their subsequent nonradiative recombination with holes in the valence band and energy transfer into the inner shell of the Er 0.2 λ ν > ions. Unfortunately, deep-level relaxation spectroscopy ex = 780 nm (h ex Eg) thus far has not revealed deep centers in SMBE-grown λ ν ∼ ex = 1030 nm (h ex Eg) structures [7]. λ ν < Erbium PL intensity, arb. units 0 ex = 1300 nm (h ex Eg) The proposed mechanism of erbium ion excitation can account for the increase in the erbium PL intensity 0 0.2 0.4 0.6 0.8 1.0 with increasing pump radiation wavelength observed to Pump power P/Pmax occur in the range 1000Ð1030 nm. The fact is that band- to-band pumping of Si : Er structures generates a large Fig. 5. Erbium PL intensity vs pump power plotted for var- λ number of electronÐhole pairs, which gives rise to the ious values of the pump radiation wavelength ex.

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004 100 ANDREEV et al. onset of intense, free-carrier-mediated nonradiative REFERENCES Auger deexcitation of Er ions, thus substantially lower- 1. B. A. Andreev, A. Yu. Andreev, H. Ellmer, et al., J. Cryst. ing the efficiency of erbium PL excitation. This sce- Growth 201Ð202, 534 (1999). nario is supported, in particular, by the drop in the 2. Z. F. Krasilnik, V. Ya. Aleshkin, B. A. Andreev, et al., in erbium PL intensity at high band-to-band pump powers Towards the First Silicon Laser, Ed. by L. Pavesi, ν (h ex > Eg; see Fig. 5). As the pump photon energy S. Gaponenko, and L. Dal Negro (Kluwer Academic, decreases, the light absorption coefficient in bulk sili- Dordrecht, 2003), pp. 445Ð454. con drops sharply in the vicinity of Eg, which entails as 3. B. A. Andreev, W. Jantsch, Z. F. Krasil’nik, et al., in Pro- sharp a drop in the number of free carriers created in the ceedings of 26th International Conference on Physics of structure. Therefore, the Auger deexcitation efficiency Semiconductors ICPS-26, Edinburg (2002). decreases strongly, thereby increasing the erbium PL 4. F. Priolo, G. Franzo, S. Coffa, and A. Carnera, Phys. Rev. signal. B 57 (8), 4443 (1998). 5. O. B. Gusev, M. S. Bresler, P. E. Pak, et al., Phys. Rev. B 64, 075302 (2001). 6. J. Wagner, Phys. Rev. B 29, 2002 (1984). ACKNOWLEDGMENTS 7. V. B. Shmagin, B. A. Andreev, A. V. Antonov, et al., Fiz. This study was supported by the Russian Founda- Tekh. Poluprovodn. (St. Petersburg) 36, 178 (2002) [Semiconductors 36, 171 (2002)]. tion for Basic Research (project nos. 01-02-16439, 02- 02-16773, 02-02-06695), INTAS (project no. 01- 0468), and NWO (project no. 047-009-013). Translated by G. Skrebtsov

PHYSICS OF THE SOLID STATE Vol. 46 No. 1 2004